This volume is intended for the advanced study of several topics in mathematical statistics. The first part of the book is devoted to sampling theory (from one-dimensional and multidimensional distributions), asymptotic properties of sampling, parameter estimation, sufficient statistics, and statistical estimates. The second part is devoted to hypothesis testing and includes the discussion of families of statistical hypotheses that can be asymptotically distinguished. In particular, the author describes goodness-of-fit and sequential statistical criteria (Kolmogorov, Pearson, Smirnov, and Wald) and studies their main properties. The book is suitable for graduate students and researchers interested in mathematical statistics. It is useful for independent study or supplementary reading.
Part I title page Preface to Part 1 Samples from one-dimensional distributions Samples from multidimensional distributions Estimation of unknown parameters of distributions Sufficient statistics General methods for constructing estimators References Part II title page Preface to Part 2 General theory of hypotheses testing Asymptotic distinguishability of simple hypotheses Goodness-of-fit tests Sequential tests References Index.