Theory of Statistics

James E. Gentle Theory of Statistics Theory of Statistics 2000 2013. c James E. Gentle Theory of Statistics 2000 2013. c James E. Gentle Preface: Mathematical Statistics After teaching mathematical Statistics for several years using chalk on a black- board (and, later, smelly dry erase markers on a whiteboard) mostly doing proofs of theorems, I decided to lecture from computer slides that provide an outline of the big picture . Rather than spend class time doing proofs that are given in standard texts, I decided that time would be better spent discussing the material from a different, higher-level perspective. While lecturing from canned slides, I cannot, however, ignore certain de- tails of proofs and minutiae of examples. But what details and which minutiae? To be effective, my approach depends on an understanding between students and the instructor, an understanding that is possibly implicit. I lecture; but I. ask what is .. ?

and it is assumed that the reader has a working knowledge of measure-theory-based probability theory. Chapter 1 covers this theory at a fairly rapid pace. Theory of Statistics c 2000–2020 James E. Gentle. Preface vii The objective in the discussion of probability theory in Chapter 1, as in that

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