Lectures in mathematical statistics : parts 1 and 2 / Yu. N. Linʹkov ; translated by Oleg Klesov and Vladmir Zayats.

By:

Linʹkov, I͡U︡. N [author]

Material type: Text

TextLanguage: English Original language: Russian Series: Translations of mathematical monographs ; v. 229Publisher: Providence, R.I. : American Mathematical Society, c2005Copyright date: c2005Description: vii, 321 pages : illustrations ; 27 cmContent type:

text

Media type:

unmediated

Carrier type:

volume

ISBN:

082183732X (alk. paper)

Uniform titles:

Lekt͡s︡ii po matematicheskoi statistike. English

Subject(s):

Mathematical statistics

DDC classification:

519.5 L.Y.L 22

LOC classification:

QA276.16 .L5513 2005

Online resources:

Contents:

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.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	Main library A8	Commerce and business administration ( Finance )	519.5 L.Y.L (Browse shelf(Opens below))	1	Available		00005338

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.

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