Lin Z.Y., Lu C.R. — Limit theory for mixing dependent random variables :: Электронная библиотека попечительского совета мехмата МГУ

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Lin Z.Y., Lu C.R. — Limit theory for mixing dependent random variables

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Название: Limit theory for mixing dependent random variables

Авторы: Lin Z.Y., Lu C.R.

Аннотация:

For many practical problems, observations are not independent. In this book, limit behaviour of an important kind of dependent random variables, the so-called mixing random variables, is studied. Many profound results are given, which cover recent developments in this subject, such as basic properties of mixing variables, powerful probability and moment inequalities, weak convergence and strong convergence (approximation), limit behaviour of some statistics with a mixing sample, and many useful tools are provided. Audience: This volume will be of interest to researchers and graduate students in the field of probability and statistics, whose work involves dependent data (variables).

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 429

Добавлена в каталог: 03.02.2006

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Предметный указатель

$(\alpha,\beta)$ -mixing      1.2
$\alpha$ -mixing      1.1 6.2
$\alpha$ -mixing random field      6.1 6.2
$\alpha_{*}$ -mixing random field      6.1
$\beta$ -mixing      1.1
$\psi$ -mixing      1.1
$\rho$ -mixing      1.1 6.2
$\rho$ -mixing random field      6.2
$\varphi$ -mixing      1.1 6.2
$\varphi^{*}$ -mixing      13.1
*-mixing      1.1
Absolutely regular      1.1 6.2
Absolutely regular random field      6.2
Additive functional of Markov process      14.3
Bernstein inequality      11.1 12.4
Berry — Esseen inequality      7.1
Berry — Esseen inequality for U-statistic      13.1
Bisection lemma      6.2
Bounds of covariances      1.2
Bounds of the variances of partial sums      2.1
Central Limit Theorem (CLT)      3
Central limit theorem (CLT) for $\alpha$ -mixing random field      6.1
Central limit theorem (CLT) for $\rho$ -mixing random field      6.1
Central limit theorem (CLT) with infinite variance      3.3
Central limit theorem (CLT), necessary and sufficient condition      3.1
Central limit theorem (CLT), sufficient condition      3.2
Complete convergence      8.3 8.4 8.5
Complete convergence for $\alpha$ -mixing sequence      8.5
Complete convergence for $\rho$ -mixing      8.4
Complete convergence for $\varphi$ -mixing      8.3
Density function      13.3
Empirical process      12
Error variance in linear model      13.2
Exponential inequality      10.1
Gaussian sequence      14.2
Ibragimov — Linnik — Iosifescu conjecture      5.2
Increments of partial sum      10
Increments of partial sum of $\varphi$ -mixing sequence      10.1
Increments of partial sum of $\varphi$ -mixing sequence with finite p-order moment      10.1
Increments of partial sum of $\varphi$ -mixing sequence with moment generation function      10.1
Inequality of tail probability      2.2
Inequality of the moments of maximum partial sums      2.2
Inequality of the moments of partial sums      2.2
Kernel estimates of density function      13.3
Lacunary trigonometric series      14.1
Law of the iterated logarithm      9.2
Levy — Prohorov distance      7.2
Metric entropy condition      6.2
Moduli of continuity of empirical process      12.4
Moduli of continuity of empirical process with $\alpha$ -mixing sample      12.4

Moduli of continuity of empirical process with $\varphi$ -mixing sample      12.4
Nearest neighbor estimates of density function      13.3
Nonuniformly $\varphi$ -mixing      6.2
Nonuniformly $\varphi$ -mixing random field      6.2
Ottaviani inequality      2.2
Prohorov problem      8.6
Random field      6.1 6.2
Rate of convergence      7
Rate of convergence in distribution      7.1
Rate of convergence in distribution for $\alpha$ -mixing sequence      7.1
Rate of convergence in distribution for $\rho$ -mixing sequence      7.1
Rate of weak convergence      7.2
Rate of weak convergence for $\alpha$ -mixing sequence      7.2
Rate of weak convergence for $\varphi$ -mixing sequence      7.2
Rate of weak convergence for absolutely regular sequence      7.2
Set indexed empirical process      12.3
Set-indexed partial sum process      6.2 6.3
Slice      6.2
Slowly varying function      2.1 App.
Strong approximation      9
Strong approximation for $\alpha$ -mixing random field      11.2
Strong approximation for $\varphi$ -mixing random field      11.1
Strong approximation for additive functional of Markov process      14.3
Strong approximation for empirical process      12.3
Strong approximation for error variance estimations in linear model      13.2
Strong approximation for Gaussian sequence      14.2
Strong approximation for lacunary trigonometric series      14.1
Strong approximation for U-statistic      13.2
Strong Law of Large Numbers      8.2
Strong law of large numbers for U-stalistic      13.1
Sufficient condition for weak in variance principle      3.2
Symmetric $\varphi$ -mixing random field      6.2
Thickness      6.2
Totally bounded      6.2
Totally bounded with inclusion      6.2
U-statistics      13.1
Uniform empirical process      12.1
Uniformly integrablity      2.1
Uniformly mixing      1.1
Unrestricted $\rho$ -mixing sequence      6.1
Vapnik — Cervonenkis class      6.2
von Mises statistics      13.1
Weak convergence      3 4 5
Weak convergence for $\alpha$ -mixing sequence      3
Weak convergence for $\rho$ -mixing sequence      4
Weak convergence of empirical process      12.1
Weak in variance principle for error variance estimations in linear model      13.2
Weak in variance principle for U-statistics      13.1
Weak in variance principle when variance is finite      4.1 5.1
Weak in variance principle when variance is infinite      3.3 4.4
Weak law of large number      8.1

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