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.
Uppsala: Acta Universitatis Upsaliensis, 2014. , 47 p.
2014-09-26, Polhemsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)