Toward the History of the St.Petersburg School of Probability and Statistics. IV. Characterization of Distributions and Limit Theorems in Statistics.

Research output

Abstract

This is the fourth article in a series of surveys devoted to the scientific achievements of the Leningrad—St. Petersburg School of Probability and Statistics from 1947 to 2017. It is devoted to studies on the characterization of distributions, limit theorems for kernel density estimators, and asymptotic efficiency of statistical tests. The characterization results are related to the independence and equidistribution of linear forms of sample values, as well as to regression relations, admissibility, and optimality of statistical estimators. When calculating the Bahadur asymptotic efficiency, particular attention is paid to the logarithmic asymptotics of large deviation probabilities of test statistics under the null hypothesis. Constructing new goodness-of-fit and symmetry tests based on characterizations is considered, and their asymptotic behavior is analyzed. Conditions of local asymptotic optimality of various nonparametric statistical tests are studied.

Original languageEnglish
Pages (from-to)36-53
Number of pages18
JournalVestnik St. Petersburg University: Mathematics
Volume52
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

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Characterization of Distributions
Asymptotic Efficiency
Statistical test
Limit Theorems
Bahadur Efficiency
Large Deviation Probability
Statistics
Local Optimality
Asymptotic Optimality
Kernel Density Estimator
Equidistribution
Non-parametric test
Admissibility
Linear Forms
Goodness of fit
Null hypothesis
Test Statistic
Optimality
Logarithmic
Regression

Scopus subject areas

  • Mathematics(all)

Cite this

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