Lectures in mathematical statistics : parts 1 and 2 /
Linʹkov, I͡U︡. N.
Lectures in mathematical statistics : parts 1 and 2 / Yu. N. Linʹkov ; translated by Oleg Klesov and Vladmir Zayats. - vii, 321 pages : illustrations ; 27 cm. - Translations of mathematical monographs, v. 229 0065-9282 ; .
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.
082183732X (alk. paper)
2005052661
Mathematical statistics.
QA276.16 / .L5513 2005
519.5 / L.Y.L
Lectures in mathematical statistics : parts 1 and 2 / Yu. N. Linʹkov ; translated by Oleg Klesov and Vladmir Zayats. - vii, 321 pages : illustrations ; 27 cm. - Translations of mathematical monographs, v. 229 0065-9282 ; .
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.
082183732X (alk. paper)
2005052661
Mathematical statistics.
QA276.16 / .L5513 2005
519.5 / L.Y.L