Asymptotic Properties of Koenker-Bassett Estimator in Regression Model with Long-Range Dependence

被引：0

作者：

Ivanov, Alexander V. ^{[1
]}

Savich, Irina N. ^{[1
]}

机构：

[1] Natl Tech Univ Ukraine, Kiev Polytech Inst, UA-03056 Kiev, Ukraine

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2011年 / 40卷 / 19-20期

关键词：

Asymptotic normality; Hermite polynomials; Hermite rank; Koenker-Bassett estimator; Long-range dependence; Spectral measure of regression function;

D O I：

10.1080/03610926.2011.581178

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This article deals with asymptotic distribution of Koenker-Bassett estimator in continuous time regression model with long-range dependent noise. It is proved that the asymptotic distribution of the normed estimator coincides with asymptotic distribution of the integral of an indicator random process generated by the random noise weighted by regression function gradient. A theorem is formulated also on asymptotic normality of the last integral.

引用

页码：3555 / 3568

页数：14

共 28 条

[1] Continuous-time stochastic processes with cyclical long-range dependence
Anh, VV
Knopova, VP
Leonenko, NN
[J]. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 2004, 46 (02) : 275 - 296
[2] Beran J., 1994, Statistics for Long-Memory Processes
[3] Billingsley Patrick, 1999, Convergence of probability measures, V2nd
[4] CONVERGENCE OF DISTRIBUTIONS GENERATED BY STATIONARY STOCHASTIC PROCESSES
DAVYDOV, YA
[J]. THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1968, 13 (04): : 691 - &
[5] Doukhan P., 2003, Theory and applications of long-range dependence
[6] Grenander U, 1957, Statistical Analysis of Stationary Time Series
[7] Huber P., 2011, ROBUST STAT
[8] Huber P. J., 1967, P 5 BERK S MATH STAT, V1, P221
[9] Ibragimov I. A., 1978, GAUSSIAN RANDOM PROC, V9
[10] Robust Estimators in Non-linear Regression Models with Long-Range Dependence
Ivanov, A.
Leonenko, N.
[J]. OPTIMAL DESIGN AND RELATED AREAS IN OPTIMIZATION AND STATISTICS, 2009, 28 : 193 - +

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