On Confidence Intervals and Two-Sided Hypothesis Testing

Sammanfattning: This thesis consists of a summary and six papers, dealing with confidence intervals and two-sided tests of point-null hypotheses.In Paper I, we study Bayesian point-null hypothesis tests based on credible sets. A decision-theoretic justification for tests based on central credible intervals is presented.Paper II is concerned with a new two-sample test for the difference of mean vectors, in the high-dimensional setting where the number of variables is greater than the sample size. A simulation study indicates that the proposed test yields higher power when the variables are correlated. Computational aspects of the test are discussed.In Paper III, we discuss randomized confidence intervals for a binomial proportion. How some classical intervals fare is compared to how a recently proposed interval fares, in terms of coverage, length and sensitivity to the randomization.In Paper IV, a level-adjustment of the Clopper-Pearson interval for a binomial proportion is proposed. The adjusted interval is shown to have good coverage properties and short expected length.In Paper V we study the cost of using the exact Clopper-Pearson interval rather than shorter approximate intervals, in terms of the increase in expected length and the increase in sample size required to obtain a given length. Comparisons are made using asymptotic expansions.Paper VI deals with exact confidence intervals and point-null hypothesis tests for parameters of a class of discrete distributions. A large class of intervals are shown to lack strict nestedness and to have bounds that are not strictly monotone and typically also discontinuous. The p-values of the corresponding hypothesis test are shown to lack desirable continuity properties, and to typically also lack certain monotonicity properties.