Resampling Methods for Checking Models and Statistical Hypotheses

Permutation tests: conditional limit theorems and multivariate applications Helmut Strasser (Wien) In this talk limit theorems for the conditional distributions of linear test statistics are presented. The assertions are conditioned on the sigma-field of permutation symmetric sets. The limit theorems are concerned both with the conditional distributions under the hypothesis of randomness and under general contiguous alternatives with independent but not identically distributed observations. The proofs are based on results on limit theorems for exchangeable random variables. The limit theorems under contiguous alternatives are consequences of a LAN-result for likelihood ratios of symmetrized product measures. The results have implications for statistical applications. By example it is shown that minimum variance partitions which are defined by observed data (e.g. by LVQ) lead to asymptotically optimal adaptive tests for the k-sample problem. Decision-theoretic properties of partitioned sample spaces Klaus Pötzelberger (Wien) Let E = (Ω,F , (Pt)t∈T ) denote an experiment. The complexity of the experiment may be reduced by replacing F by a finite field F̃ ⊆ F , which leads to the experiment F = (Ω, F̃ , (Pt)t∈T ). F̃ is identified with a finite partition B = (B1, . . . , Bm) of Ω. A reduced experiment which is maximal with respect to the information semiorder on the set of all reduced experiments with the size of the corresponding partition being at most m is called admissible. We give characterizations of admissible experiments and of the corresponding field F̃ . The problem of characterizing admissible subfields is directly connected with the following problem. Let P be a Borel probability measure on a suitable Banach space ( IR|T | if T is finite). Characterize the maximal elements μ ∈M(P,m) with respect to the Bishop-De Leeuw order , where μ ∈M(P,m) if and only if μ P and |supp(μ)| ≤ m. The results are relevant for procedures based on a data-driven partition of the sample space. Statistical challenges in survival and event history analysis: complicated sampling frames and summary statistics Niels Keiding (Kobenhavn) This talk presented a series of examples of survival and event history analysis under complicated sampling frames, all initiated by taking a cross-sectional sample through a population subject to morbidity and mortality in calendar time. I also gave an introduction to current work (lead by P.K.Andersen in our department) using regression analysis of pseudo-observations (known from jackknife methodology) to obtain regression models for secondary summary measures such as transition probabilities in multi-state models. The complicated sampling frames were all illustrated by Lexis diagrams. Three examples concerning incidence were given: incidence estimation from current status data retrospective incidence estimation using inverse probability weighted estimates based on independent survival information