Selected topics in characteristic functions
著者
書誌事項
Selected topics in characteristic functions
（Modern probability and statistics）
VSP, 1999
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注記
Bibliography: p. 335-349
Includes indexes
内容説明・目次
内容説明
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
目次
- Part 1 Basic properties: definition and elementary properties
- continuity theorems and inversion formulas
- criteria
- inequalities
- characteristic functions and movements, expansion of characteristic functions, asymptotic behaviour
- unimodality
- analycity of characteristic functions
- multivariate characteristic functions. Part 2 Inequalities: auxiliary results
- inequalities for characteristic functions of distributions with bounded support
- moment inequalities
- estimates for the characteristic functions of unimodal distributions
- estimates for the characteristic functions of absolutely continuous distributions
- estimates for the characteristic functions of discrete distributions
- inequalities for multivariate characteristic functions
- inequalities involving integrals of characteristic functions
- inequalities involving differences of characteristic functions
- estimates for the positive zero of a characteristic function. Part 3 Empirical characteristic functions: definition and basic properties
- asymptotic properties of empirical characteristic functions
- the first positive zero
- parameter estimation
- non-parametric density estimation 1
- non-parametric density estimation 2
- tests for independence
- tests for symmetry
- testing for normality
- goodness-of-fit tests based on empirical characteristic functions.
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