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Mathematical Statistics - ETH Z

Mathematical StatisticsSara van de GeerSeptember 20102 Contents1 Some notation and model assumptions .. Estimation .. Comparison of estimators: risk functions .. Comparison of estimators: sensitivity .. Confidence intervals .. confidence sets and tests .. Intermezzo: quantile functions .. How to construct tests and confidence sets .. An illustration: the two-sample problem .. normality .. nonparametric test .. of Student s test and Wilcoxon s test .. How to construct estimators .. estimators .. method of moments .. methods .. 232 Decision Decisions and their risk .. Admissibility .. Minimaxity .. Bayes decisions .. Intermezzo: conditional distributions .. Bayes methods .. Discussion of Bayesian approach (to be written) .. Integrating parameters out (to be written).

10 CHAPTER 1. INTRODUCTION The class F 0 is for example modeled as the class of all symmetric distributions, that is F 0:= {F 0(x) = 1 −F 0(−x),∀x}.(1.2) This is an infinite-dimensional collection: it is not parametrized by a finite dimensional parameter.

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