AN EXTENSION OF LAI AND WEI LAW OF THE ITERATED LOGARITHM WITH APPLICATIONS TO TIME-SERIES ANALYSIS AND REGRESSION

被引：8

作者：

CHEN, ZG

机构：

[1] Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1990年 / 32卷 / 01期

基金：

中国国家自然科学基金;

关键词：

double array; finite Fourier transform; law of the iterated logarithm; least squares estimate; linear regression; linear series; tapered data;

D O I：

10.1016/0047-259X(90)90071-O

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：

For a double array aN = (aNn)-∞<n<∞ of nonrandom constants and independent random variables εn, under some conditions, Lai and Wei (1982, Ann. Statist. 10 320-335) proved the law of the iterated logarithms for SN = ΣnaNnεn. This paper extends this law to the case of S ̃N = ΣnaNnun, where {un} is a linear series of the form un = Σj=0∞κjεn-j. As applications of the theorem we establish the law of the iterated logarithm for finite Fourier transforms in spectral analysis and for least squares estimates in regression models in which the random disturbances form a linear series. © 1990.

引用

页码：55 / 69

页数：15

共 5 条

[1]

Brillinger D., 1981, TIME SERIES DATA ANA

[2]

CHEN ZG, 1988, ADV APPL PROBAB, V20, P295

[3] STRONG CONSISTENCY OF LEAST-SQUARES ESTIMATES IN MULTIPLE-REGRESSION .2. [J].