Construction Of Confidence Intervals.pdf

Christoph Dalitz's technical report, "Construction of Confidence Intervals" (2017-01), explores methods to create confidence intervals for various estimators, beyond the typical "two sigma" interval for the mean value. It covers:

1. Introduction: Confidence intervals measure the accuracy of estimated parameters. Different approaches exist, including frequentist, likelihood ratio, and Bayesian (highest posterior density).

2. Basic Terms: The report defines estimators, coverage probability, likelihood ratio, and posterior density. It discusses maximum likelihood (ML) estimation and its properties.

3. Binomial Proportion: Simple formulas or algorithms compute confidence intervals for binomial proportions. Evaluation criteria include coverage probability and interval length.

4. Mean Value: Similar to binomial proportions, simple methods exist for mean values. The report discusses the impact of true parameter values on coverage probability.

5. Maximum Likelihood Estimators: For these estimators, the confidence interval for the mean value can be used, requiring an estimation of the estimator variance (Hessian matrix or Jackknife variance).

6. Arbitrary Estimators: The bootstrap method is universally applicable but may have a poorer coverage probability compared to other methods.

7. Monte Carlo Simulations: The report evaluates different methods' coverage probability and interval length through simulations.

8. Recommendations: It provides guidelines on which confidence interval method to use based on the specific case.