TY - BOOK AU - Linʹkov,I͡U︡N. TI - Lectures in mathematical statistics: parts 1 and 2 SN - 082183732X (alk. paper) AV - QA276.16 .L5513 2005 U1 - 519.5 22 PY - 2005/// CY - Providence, R.I. PB - American Mathematical Society KW - Mathematical statistics N1 - Includes bibliographical references and index; pt. 1. Samples from one-dimensional distributions -- Empirical distribution function and its asymptotic behavior -- Sample characteristics and their properties -- Order statistics and their properties -- The distributions of some functions of Gaussian random vectors -- Samples from multidimensional distributions -- Empirical distribution function, sampling moments, and their properties -- Sampling regression and its properties -- Estimation of unknown parameters of distributions -- Statistical estimators and their quality measures -- Estimation of a location parameter -- Estimation of a scale parameter -- The Cramér-Rao inequality and efficient estimators -- The Cramér-Rao inequality for a multidimensional parameter -- Integral inequalities of Cramér-Rao type -- Sufficient statistics -- Sufficient statistics and a theorem on factorization -- Sufficient statistics and optimal estimators -- General methods for constructing estimators -- Method of moments -- The maximum likelihood method -- Bayes and minimax methods -- Confidence intervals and regions -- pt. 2. General theory of hypotheses testing -- Testing two simple hypotheses -- Distinguishing a finite number of simple hypotheses -- Distinguishing composite hypotheses -- Asymptotic distinguishability of simple hypotheses -- Statistical hypotheses and tests -- Types of the asymptotic distinguishability of families of hypotheses. The characterization of types -- Complete asymptotic distinguishability under the strong law of large numbers -- Complete asymptotic distinguishability under the weak convergence -- Contiguous families of hypotheses -- Goodness-of-fit tests -- The setting of the problem. Kolmogorov test -- The Pearson test -- Smirnov test -- Other goodness-of-fit tests -- Sequential tests -- Bayes sequential tests of hypotheses -- Wald sequential tests -- The optimality of a sequential Wald test UR - http://www.loc.gov/catdir/toc/fy0604/2005052661.html UR - http://repository.fue.edu.eg/xmlui/handle/123456789/2692 ER -