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I am experimenting with the eigenfaces algorithm, and I am unclear on a number of the finer points of the technique. For starters, consider the matrix of images used to do the initial PCA. Is it "better" to have only images of different individuals in that matrix? Or is it useful to include multiple images of the same ...
I am involved in a project that is attempting to measure the impacts of person-level, county-level and medical service area-level predictors on individual probability of returning to a hospital within a year window. I see this as a 3 level random effect logistic regression model. There are lots of predictors, probabl...
I do not think that the following problem can be solved with k-means clustering. I am not sure though. Okay, let me describe the problem. I need to find a way or an algorithm that groups members of a given data set (of positive integers) so that the difference between group means is minimized (not maximized, as usual)....
Currently, I was wondering can we just compare two random variables just like the way we compare two real numbers? Does that make sense? Like for instance, $X$ and $Y$ are two random variables, does $X>Y$ mean something? Or is it plainly nonsense? Anyone has some ideas? Your opinion is greatly appreciated!
I have 5 predictors in a multiple regression model with samples sizes that range from 157 to 330 for each predictor. Given the variation in sample size, is it better to use the adjusted R-squared value rather than the R-squared value.
I systematically chose rare words from three groups of texts (#1, #2 and #3) (the rare words within each group are different, but some rare words may appear in more than one group). Then, for each rare word, I attempted to found out how frequent it is in one corpus (a large, systematic aggregation of texts), called Cor...
I want to carry out Graph Clustering in a huge undirected graph with millions of edges and nodes. Graph is almost clustered with different clusters joined together only by some nodes (kind of ambiguous nodes which can relate to multiple clusters). There will be very few or almost no edges between two clusters. This pro...
I have following numbers 0.889046409368551 1.22726162946495 1.22726162946495 1.35785109728356 1.35785109728356 1.10704609982913 1.4424189950435 1.2277843378837 1.35785109728356 0.970883941918588 0.822170913920467 1.35785109728356 0.358815782262543 0.774234247460432 0.822170913920467 0.822170913920467 0.72599976...
Estimating parameters using maximum likelihood estimation (MLE) involves evaluating the likelihood function, which maps the probability of the sample (X) occurring to values (x) on the parameter space (θ) given a distribution family (P(X=x|θ) over possible values of θ (note: am I right on this?). All examples I've seen...
In simple linear regression problems, autocorrelated residuals are supposed not to result in biased estimates for the regression parameters. Can the same be said for piecewise regression? Suppose I want to fit a continuous, piecewise linear function of a single variable. Let's say for example we have data on shipping ...
In a recent exam, we were asked to justify the use of the $\chi^2(1)$ distribution in performing the Wald or Rao's score test. There was only 1 mark for this (approx. 2.5 mins worth of time). My answer was The Wald and score test statistics are based on various approximations to the log-likelihood ratio, which are ...
For one of my projects I need to find posterior probability of visiting a state S and emitting a symbol. I have built a HMM in R and later I get one observation sequence. But, I am not able to interpret the output. > # Sequence of observations > observations = c("L","L","R","R") > # Calculate posterior probablities of ...
I'm doing a research and using random variables to model a random process. I'm defining a Bernoulli random variable as a product of several other Bernoulli variables (three or more). So, I have the following as the expectation: $E[X_1]=E[X_2X_3X_4]$ I cannot assume the independence of the variables $X_i$ for any $i$....
I have performed a mixed design ANOVA with time (pre-post) and group (treatment vs control) as variables. I'm wondering if it's sensible to use between subjects difference adjusted CIs (from Baguley, 2012) in the interaction plot below. What I want to emphasize is the group difference at post-test (and of course non-si...
Suppose we have the following probabilistic graphical model: $L \rightarrow X, L \rightarrow Y, F \rightarrow Y, X \rightarrow D, Y \rightarrow D$. That is, the joint is: $P(D,X,Y,L,F) = P(D|X,Y)P(X|L)P(Y|L,F)P(L)P(F)$. Here $L,F,D$ are discrete, $X,Y$ are continuous random variables (having proper pdf's). I want t...
I'm a programmer, with a decent but not-expert knowledge of stats, and I'm working through these instructions for how to create funnel plots. I know that there are better ready-made tools (e.g. R) for generating funnel plots, but these instructions are helping to understand the basics of funnel plots. So, my question:...
This may for sure be a basic question but suppose a model \begin{equation} y = \alpha \times r^\gamma \times \varepsilon \end{equation} the parameters $\alpha$ and $\gamma$ are of interst for me (and $\varepsilon$ is the standard error term). so my first intention was do take the $log()$ of the function. however, i ...
I am trying to fit a Gumbel distribution to a set of N i.i.d. data points. I was wondering whether there is a conjugate prior to infer the two parameters of the Gumbel pdf.
I have set of random values with the same distribution $y_1, \ldots, y_N$ $$T = \frac{1}{N}\sum_{j = 1}^{N} y_j$$ I want to find the confidence interval for the mathematical expectation $E(Y)$ I can use an approximation: $T∼N(μ,\frac{\sigma^2}{N})$, where $\sigma=\frac{\sum^N_{i=1}(y_i−T)^2}{N−1}$. This approximat...
Following up on "How to evaluate quality of probability estimator for Bernoulli experiments?", I want to visualize the quality of an estimator for probability forecasting using a Reliability Diagram. I do not however want to put the observations into "bins", which seems to me an unprecise estimation, but rather estimat...
We are trying to create auto-correlated random values which will be used as timeseries. We have no existing data we refer to and just want to create the vector from scratch. On the one hand we need of course a random process with distribution and its SD. On the other hand the autocorrelation influencing the random proc...
Last week I had an interesting discussion with a good friend of mine. He had been playing some online poker and suggested that there is a relationship between new subscription/additional money transfer and the cards that you're dealt, i.e. you get good cards to get hooked. The sites would probably be risking a lot if t...
I'm a programmer, with a decent but not-expert knowledge of stats, and I'm working through these instructions for how to create funnel plots. I understand from a previous question that the standard error in these instructions is being calculated using p(1-p) (in step 4), because these are events and therefore follow a...
I have data for a test on three groups. The measured variable is ratio scaled. The R code is g1a<-c(7, 3, 40) g2a<-c(1,1,2) g3a<-c(0,0,0) Since the sample is small and normality cannot be guaranteed, I run a Kruskal Wallis test to check for significance: l<-list(g1a,g2a,g3a) kruskal.test(l) The p-value is 0.02336, wh...
It is postulated that one of the main issue is to find an appropriate covariance structure for repeated measures designs [Ref1]. SAS' PROC MIXED contains a number of covariance structures. Despite "many choices among models to fit to a given data set in the mixed model setting... [and] we must always remember that all ...
A researcher knows that the probability that a person will respond his letter is 10% If the researcher sends a post-paid letter the probability that the reciever will respond is 40%. The researcher sends 5 post-paid letters and 5 non post-paid letters. What is the probability that he recieves less then 3 responses? An...
I've been assigned to do a cross-class project between political science and math about the behavior of voters in a democratic state. More specifically, I'm focusing on a party from a national election in 2007, where I have made a table consisting of two rows – mandates and news about that party – and one column for ea...
A researcher knows that the probability that a questionnaire will be reponded by mail is 40%. He wants to be 99% sure he will get at least 200 responded questionnaires back. How many questionnaires must he send by mail to be 99% sure he will get at least 200 answers?
I am looking for guidelines on how to interpret residual plots of glm models. Especially poisson, negative binomial, binomial models. What can we expect from these plots when the models are "correct"? (for example, we expect the variance to grow as the predicted value increases, for when dealing with a Poisson model)...
I wish to deal with over dispersion of a Poisson model. Negative binomial (glm.nb), and quasi likelihood models (family=quasi in glm) do not offer a flexible enough structure of the variance-vs-mean relationship. I would like to fit a full third order model between mean and variance, and could not find an R function ...
I have a least square problem with two different inequality problems. I can not use NNLS because its just solves least square problem with equality and inequality problems or just one inequality constraint. Can I use NNLS or any other algorithm or R package that I can solve this least square problem?How can I use limS...
I can't get the same results in R as in GraphPad Prism for repeated measures anova. The experiment was a stimulation time course, so I have as DV=response and as factor "time" within groups, also I add a factor sample for each experiment data <- read.csv("http://dl.dropbox.com/u/4828275/datos.csv") options(contrasts=c(...
Let $X_1,X_2$ be independent distributed with cdfs $F_1(x),F_2(x)$, so that $$\overline F_i(x) := 1 - F_i(x) = x^{-\alpha}L_i(x),\ \alpha \geq 0 \>,$$ where $L_i(x)$ is a slowly varying function, that is, it satisfies $L(tx)/L(x) \to 1$ as $x \to \infty$ for all $t > 0$. For $0<\delta<\frac{1}{2}$ I have the following...
I'm reading this book. Here, he gives me a method for calculating the mean: Here he introduces a new method of calculating the mean through histogram: He says that now we will count and index the samples in the histogram, this list: {7, 8, 0, 9, 2, 10, 4, 1, 6, 0, 8, 7, 6, 0, 0} Is going to be counted and it will ...
I am performing a meta-analysis. I have a subgroup made only of 2 studies and they show opposite results. The 1st has excellent outcomes the 2nd very bad ones. Is it true that I am not allowed to compute the data from these two (different) studies under a random-effect model? I have been told that it is methodologicall...
I have the following problem: I want to minimize a least square problem with non-linear restrictions. The start model has the following form: $$w^*=\text{min arg}_w \sum_{i=1}^{N} (y_i-\sum_{j=1}^3 w_jx_{ij})^2$$ where $w \in R.$ I minimized error at above model using least-square method. My model is now more complicat...
I have a collection of data, which I originally thought was normally distributed. Then I actually looked at it, and realised it wasn't, mostly because the data is skewed, and I also did a shapiro-wilks test. I'd still like to analyse it using statistical methods, and so I'd like to hypothesis test for skew-normality. S...
I'm sorry if this is some kind of standard exercise, but I just don't know how to search for it. I have infinite amount of samples and I can measure two properties $A$ and $B$ for each sample. Chance to measure $A$ is $P(A)$ and for $B$ it's $P(B)$, both properties are independent. I take N samples and on $a$ of those ...
from a deck of 52 cards, 9 cards are drawn at random without replacement. If X and Y are the number of hearts and diamonds respectively. What is the joint probability of X and Y and also what is the probability of X being greater than Y?
Heloo, pleas help me How to read files (text and excell) into R ? pleas write full instruction. Thank for help
If $X$ and $Y$ are two independent random numbers from the interval $(0,1)$, then what is the PDF of $U = -2 \ln X$ and $V = -2\ln Y$?
I'm reading the IPCC report on climate change from 2007. In their uncertainity guide they make a distinction between likelihood and levels of confidence. What's the difference between the terms? http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-uncertaintyguidancenote.pdf
What is the difference between linear regression and logistic regression? When would you use each?
Five months ago, jbowman posted a very useful answer to estimate the break point in a broken stick model with random effects in R. I never use "computing" like ifelse and I would like to estimate two break points. I should write two other functions like b1 and b2 but I don't know how. Can someone please tell me how to ...
The Wikipedia article of the log-normal distribution says If $X$ is a random variable with a normal distribution, then $Y = \exp(X)$ has a log-normal distribution; likewise, if $Y$ is log-normally distributed, then $X = \log(Y)$ is normally distributed. (This is true regardless of the base of the logarithmic fu...
I was wondering, what is the meaning of operators in anova or regression formulas in R For example "+" aov <- aov(x~time+sample, data=data) -> repeated mesures anova? "*" aov <- aov(x~time*sample, data=data) -> two way anova? "/" aov <- aov(x~time/sample, data=data) -> ? ":" aov <- aov(x~time:sample, data=data) -> ? ...
I'm a computer scientist working in data mining. It's no secret to say that computer scientists are fairly poor at doing systematic experimental design and evaluation - the use of p-values and confidence estimates is considered advanced :). What I'd like to know if there are good courses/material to teach computer sci...
Introduction I am aiming to forecast the annual growth rates for a number of macroeconomic indicators (denote one by $Y_t$). One of the tasks is to test the forecasting performance of rival time series models with and without exogenous variables ($X_t$, a $T\times k$ matrix). The list of rival models include: AR(I)MA...
I'd like to understand the Baum-Welch algorithm. I liked this video on the Forward Backward algorithm: http://www.youtube.com/watch?v=7zDARfKVm7s&feature=related I'm having trouble coming up with good resources for Baum-Welch. Any ideas?
Suppose I have a bunch of people who did a few tests (let's call it tests A). Now I'll do a second test (test B) in order to categorize these people into two categories (that have a pre-defined "true" answer). Note that score from test A can only predict the signal-to-noise ratio of test B. I.e you can't use score f...
Textbooks typically have nice example plots of of the basis for uniform splines when they're explaining the topic. Something like a row of little triangles for a linear spline, or a row of little humps for a cubic spline. This is a typical example: http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/...
Suppose that the random variables $Y_1, ..., Y_n$, satisfy $Y_i = \beta \cdot x_i + \epsilon_i$ for $i = 1,...,n$ where $\beta$ is a constant, $x_1,...,x_n$, are constants, and $\epsilon_1,...,\epsilon_n$, are independent and identically distributed random variables with $\epsilon_i \sim N(0,\sigma^2)$, where $\sigma^2...
This question may well be too open-ended to get a definitive answer, but hopefully not. Machine learning algorithms, such as SVM, GBM, Random Forest etc, generally have some free parameters that, beyond some rule of thumb guidance, need to be tuned to each data set. This is generally done with some kind of re-sampling ...
I would like to gain a conceptual understanding of Root Mean Squared Error (RMSE) and Mean Bias Deviation (MBD). Having calculated these measures for my own comparisons of data, I've often been perplexed to find that the RMSE is high (for example, 100 kg), whereas the MBD is low (for example, less than 1%). More spec...
I am searching tutorial for support vector regression in R. I found this and manual for e1071 package. But there is few explanation how to set parameters, like choose kernels, choose regression, not classification. Any material is appreciated.
I am looking to divide the 50 US states into n regions. The requirements in dividing are: Each state will be assigned a value The state values in each region should sum to make even group totals (as closely as possible). Which seems to make this a bin packing problem variation. The states in each region need to be geo...
Let $X \sim N_q(\mu, \Sigma)$ with a Normal-Inverse-Wishart prior on $(\mu, \Sigma)$ i.e. $(\mu, \Sigma) \sim N_q(\mu | m, \Sigma / k) IW_q(\Sigma | \nu, \Lambda)$ where we are using the Inverse Wishart paramaterization that gives $E [\Sigma] = \frac{\Lambda^{-1}}{\nu - q -1}$. I need the marginal distribution of $X$; ...
If I have done a (binomial) logistic regression. Is it then possible from the coefficients to calculate a percentage of how much each of the variables affects the dependent variable. Say that we have for example var1: 0.635, var2: 0.245, var3: 1.243. If we know that the depends variable Y in the data is 1 at 0.64 of th...
Assume last year I commuted to work in a taxi, and suppose if there are $n$ taxis in the fleet I used. If I took one of these taxis every trip at random and with replacement, then what is the number of trips I need to make in order to use every taxi in the fleet?
I'd like to see an extension of this discussion of the age-old chi-sq vs. Fisher's exact test debate, broadening the scope a bit. There are many many tests for interactions in a contingency table, enough to make my head spin. I'm hoping to get an explanation of what test I should use and when, and of course an explanat...
I moedelled following ARIMA Process which I also smoothed. abc1 <- (arima.sim(n = 1400, list(ar = c(0.3, 0.2, 0.15, 0.1, 0.1, 0.1)), sd = sqrt(0.5))) plot(abc1) abc2 <- SMA(abc1, n=360) plot(abc2) My aim is it to add a component for mean-reversion to describe a business cycle model. Ideas? thanks, F!
I regularly encounter the following scenario: I am presented with a set, $\mathcal{S}$, of $i$ items. I am assured that $d$ of the $i$ items possess a particular property, $d'$ - and that the rest, $(i-d)$, do not. So the items are in 2 piles: $d'$ and non-$d'$. (For context, let's say that $i$ is known to be 1,000,...
I have a dataset for around 40k firms over fiscal years 1950-2011 with about 430k firm-years. If I'm not mistaken I have panel-data. In addition, the firms are nested within 9 industries. I created a unique identifier ticn for each firm. Years are indicated by fyear. For now my variables of interest are yearly sales sa...
I have become interested in statistics, but I must admit that it has been a long time since I have used math seriously. Sometimes I understand what equations mean, but sometimes I can't follow them. I like the answer given here that uses the image with an arrow: Conceptual understanding of root mean squared error and ...
I'm training a Multi-class LDA classifier with 8 classes of data. While performing training, I get a warning of: "Variables are collinear" I'm getting a training accuracy of over 90%. I'm using scikits-learn library in Python do train and test the Multi-class data. I get decent testing accuracy too(about 85%-95%). I d...
In the spirit of What statistical blogs would you recommend? I propose a collection of machine learning blogs worth reading.
Consider multivariate time series models that estimate potentially time-varying conditional means, variances, and correlations (one type of model might be a VAR(p)+Garch(1,1)+DCC Gaussian Copula model). I will simulate from one "true" distribution and compare other potential models to it. I don't particularly care abou...
I'm running a generalized linear model (quasi-poisson regression) as a cron job in R that trains on data from an SQL query. The SQL query pulls data from the last 30 days. Depending on the sample of data from the last 30 days, the regression coefficients of course change. As a result, I'm then writing the regression co...
Suppose you have 40 different books (20 math books, 15 history books, and 5 geography books). Let M = math books, H = history books, G = geography books You pick 5 books at random, with replacement, one at a time. What is the probability that you've picked books from at most two disciplines? I know this is basic, but.....
I have been reading the book, Good to Great by Jim Collins. It says that you should focus on information that "cannot be ignored," and that you should focus on the right "denominator." I thought it would be good to measure "Average Growth Rate per Producing Entity." If we are providing value and support, we would exp...
I have a matrix with 1024 features and 10000 samples with a label vector of three different classes. I use R MASS library lda function to compute the model and get the coefficients for linear discriminants: > library (MASS) > > ldamodel = lda(data$X, data$y) > head (ldamodel$scaling) LD1 LD2 V5 -...
I am using "smooth.spline" in R. Here is a snippet from the documentation: http://stat.ethz.ch/R-manual/R-patched/library/stats/html/smooth.spline.html smooth.spline {stats} R Documentation Fit a Smoothing Spline Description Fits a cubic smoothing spline to the supplied data. Usage smooth.spline(x, y = NULL, w = NULL...
We have conducted a repeated measures experiment in which we have registered the response time (RT) of each subject in 21 trials in each of 2 conditions. I have some questions related to the best analysis we can conduct... First, to reduce individual variability between subjects, we have standardize "within subjects",...
I have the following linear model: $$w^*=\text{arg min}_w\sum_{i=1}^N \bigg(Y_i-\sum_{j=1}^M X_{i,j}\times w_j\bigg)^2$$ Let $T \in N^*$ and $e_i=|Y_i-\sum_{j=1}^M X_{i,j}\times w_j|$. It's possible using logistic regression to predict which errors will be less than $T$ (i.e., $e_i<T$) and greater or equal with $T$ (i...
I have two random variables: $x = N(0, \sigma^2)$ and $y =U[0, b]$. I need to compute $E(x/(1+y))$. How does one go about doing this? They are independent so the joint pdf is just the product of the two pdfs but can the integral be computed in closed form or is this something that should just be done numerically?
I want to know what statistics should be used to measure the mixing of languages in cities in a country/state. I have samples from individuals and know the language they speak and the city they live in. The cities are not all the same size and there are 3 different language groups. The samples are taken uniformly from ...
I have three types of summary score, $a, b$ and $c$ for 200 samples. $S1, S2, S3,..., S200$ $a_{s1}, a_{s2}, ..., a_{s200}$ $b_{s1}, b_{s2}, ..., b_{s200}$ $c_{s1}, c_{s2}, ..., c_{s200}$ Each of these scores is essentially the number of times that some event occurs in the data of each sample. I wish to find groups of ...
I am comparing three different measures comprised of 10-20 items each. Each of these measures is actually a short form of a longer 40-item measure and each of the short forms shares some similar items, and thus they are quite similar. I am interested in seeing how each of these short forms are correlated with the same ...
I'm looking for some forecasting advice when dealing with seasonal time series data that has a large number of observations. By "large" I only mean a few thousand --- I'm used to such sizes in Data Mining being considered pretty small, but it seems that in time series modeling that's pretty unwieldy for many of the to...
This must come up---the forecasting of things that are stuck between 0 and 1. In my series, I suspect an auto-regression component, and also a mean-reverting component, so I want something that I can interpret like an ARIMA---but I don't want it to shoot off to 1000% in the future. Do you just use an ARIMA model as the...
Consider drawing stones from an urn with replacement. Suppose the urn contains a large number of stones, and each stone has a color, and the set of possible colors is large. Suppose $N$ stones are drawn one at a time from the urn, and replaced each time. Suppose $S$ of them have the same color, $C$. Can I write a distr...
I was just about to ask a question concerning a certain 3D data-set (each point in space has a value associated), but couldn't figure out how to visualize it for you. I can understand it myself by rotating the point set in a Matlab figure, but it would be difficult to grasp from just seeing a screenshot: (marker size ...
In R, I am using the bc function to do a box-cox transformation. What factors do I need to consider when setting p (the power argument)?
I am trying to make predictions using a random forest model in R. However I get errors since some factors have different values in the test set than in the training set. For example, a factor Cat_2 has values 34, 68, 76, etc., in the test set that do not appear in the training set. Unfortunately, I do not have control ...
Could you please shed some lights about how to interpret linear regresssion results (2-stage vs. 1 stage)? For example, I have the following: lmStage1 <- lm(y~x1) lmStage2 <- lm(residuals(lmStage1)~x2) summary(lmStage2) vs. lmAll <- lm(y~x1+x2) summary(lmAll) How do I interpret and compare the coefficients/t-stats, ...
Feel free to substitute 'journals' for any other useful portal of knowledge. I am interested in keeping an eye on new developments in machine learning, with a view to practical applications. I am not an academic seeking to publish my own work (at least not in this field), but I do want to be aware of potential new algo...
One standard approach we use when describing our data for a paper is to cut our dependent variable into tertiles and then give mean/SD or median/IQR for each tertile for continuous and percentage/number in each tertile for each category for categorical independent variables. This is fine for an overview. But I can't he...
I have measured whole-genome gene expression in two groups of animals, n=6 in each group. My goal is to detect differentially expressed genes - pretty standard analysis. The typical thing to do, and what I suspect is a situation where 'everybody does it this way because everybody does it this way' is to run limma with ...
Is it correct to say that the Hidden State Sequence in a Hidden Markov Model is a Markov Chain? Thanks
I've got to verify whether there is a significant difference in value market shares between 2 versions of packaging (A and B) of a given beverage: For the 'Packaging A' I've got a sample of 600 purchases on which I compute average 'Packaging A' purchase value as well as the average value of entire category purchase. B...
Given a set $A$ of $n=kl$ positive real numbers, let $a_{ij}$ be a random number removed from the set $A$ (without replacement) for $i=1 \dots k$ and $j=1 \dots l$. What is the distribution and expected value of the following expression? $$ \prod_{i=1}^{k} \sum_{j=1}^{l} a_{ij} $$ Note: Using a set of 30 numbers for $...
How can I enunciate this notation correctly, could you show me that, please? $$ \sum \big( {Y_{i}}-{ \hat{Y}_{i}} \big)^2 $$ Thank you very much.
In the idealized logistic model, we obtain an S-shaped curve linking each continuous IV to the DV. But in practice this S-shape infrequently occurs, making the logistic approach seem a little less superior for such types of data. Of course predicted probabilities that each observation will be "1" on the DV are usable...
I have a dataset with the following structure: Choice Bank Bank_x Customer Customer_x 0 UBS . 1 . 1 CS . 1 . 1 KZ . 1 . 0 VA . 1 . -------------------------------------- 0 UBS . 2 . ...
Is there an easy way in R to create a linear regression over a model with 100 parameters in R? Let's say we have a vector Y with 10 values and a dataframe X with 10 columns and 100 rows In mathematical notation I would write Y = X[[1]] + X[[2]] + ... + X[[100]]. How do I write something similar in R syntax?
How do I get the 95% confidence interval for ANOVA level coefficients? For comparison with a constant value, not multiple comparison (like MMC). I tried to take the coefficient's SE from the model: > m1 = lm(formula = TrendAdd ~ 0 + Migrace) > c = coef(summary(m1)) > c Estimate Std. Error t value Pr...
I think meta-analyses are a great way of exploring a hypothesis when available evidence is heterogeneous. Usually however when conducting a meta-analysis one puts aggregated data in a model, possibly losing information. Therefore I am considering gathering data from published research from the authors in order to be a...
What's a meaningful "correlation" measure to study the relation between the such two types of variables? In R, how to do it?
Given an (observed) time-series $X_t$ with $X_t\in\{1,...,n\}$, is there a statistical test for testing the null-hypothesis that $P(X_t|X_{t-1},X_{t-2},...,X_1)=P(X_t|X_{t-1})$ (i.e. the markov-property)?
I have a few questions about generalizations of the CLT and stable distributions. I'm trying to correct my understanding and make it precise. Please forgive my naivete, I am not a professional statistician :-) If I take the sum of a large enough sequence of independent R.V.'s, do they always converge to a stable distri...