Transcription of Mathematical Statistics - SfS
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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.
Statistics is about the mathematical modeling of observable phenomena, using stochastic models, and about analyzing data: estimating parameters of the model and testing hypotheses. In these notes, we study various estimation and testing procedures. We consider their theoretical properties and we investigate various notions of optimality.
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