Selected Topics in Characteristic FunctionsThe 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. |
Contents
Inequalities | 23 |
A Examples | 259 |
B Some characteristic functions | 281 |
Unsolved problems | 331 |
| 351 | |
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Common terms and phrases
absolutely continuous distribution acteristic bounded bounded variation ch.f charac characteristic func characteristic function f(t conditions of Theorem consider converges COROLLARY corresponding characteristic functions cos(tx covariance matrix Csörgő defined Denote dF(x differentiable discrete unimodal distribution function F(x e-itx empirical characteristic function empirical distribution function example exists a characteristic f²(t finite fn(t Fn(x fo(t function with characteristic hence implies inequality integer integrable interval kernel estimator Lemma Let F(x Let the conditions Let us prove lim sup m-dimensional MISE(pn(x multi-dimensional non-negative normal distribution obtain parameter pn(x positive integer probability density function proof of Theorem random variable random vector Rf(t right-hand side Ry(t satisfying the conditions sequence sin(at sin(x spherically symmetric sup f(t t₁ test statistic tic functions tion un(t underlying distribution unimodal distribution univariate Ushakov values variance virtue of Theorem σ² Ам
Popular passages
Page 340 - Heathcote, CR ( 1972). A test of goodness of fit for symmetric random variables. Austral. J. Statist. 14, 172-181.
Page 339 - FANG, KT, KOTZ, S. and NG, KW (1989). Symmetric Multivariate and Related Distributions, London and New York: Chapman and Hall.
Page 336 - Binmore, KG, and Stratton, HH (1969). A note on characteristic functions. Ann. Math. Statist. 40, 303-307.