Abstract
This report defines frequentist, likelihood ratio, and Bayesian methods for confidence intervals, applies them to binomial proportions, means, and general estimators using Hessian, Jackknife, and bootstrap variance estimation, and evaluates coverage and length via Monte Carlo simulations with R code.
Introductory texts on statistics typically only cover the classical "two sigma" confidence interval for the mean value and do not describe methods to obtain confidence intervals for other estimators. The present technical report fills this gap by first defining different methods for the construction of confidence intervals, and then by their application to a binomial proportion, the mean value, and to arbitrary estimators. Beside the frequentist approach, the likelihood ratio and the highest posterior density approach are explained. Two methods to estimate the variance of general maximum likelihood estimators are described (Hessian, Jackknife), and for arbitrary estimators the bootstrap is suggested. For three examples, the different methods are evaluated by means of Monte Carlo simulations with respect to their coverage probability and interval length. R code is given for all methods, and the practitioner obtains a guideline which method should be used in which cases.
Get this paper in your agent:
hf papers read 1807.03582 Don't have the latest CLI?
curl -LsSf https://hf.co/cli/install.sh | bash Models citing this paper 1
Datasets citing this paper 0
No dataset linking this paper
Spaces citing this paper 0
No Space linking this paper
Collections including this paper 0
No Collection including this paper