SPECTRAL ESTIMATION OF CONTINUOUS-TIME STATIONARY-PROCESSES FROM RANDOM SAMPLING

被引：26

作者：

LII, KS ^{[1
]}

MASRY, E ^{[1
]}

机构：

[1] UNIV CALIF SAN DIEGO,DEPT ELECT & COMP ENGN,LA JOLLA,CA 92093

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1994年 / 52卷 / 01期

关键词：

SPECTRAL ESTIMATION OF CONTINUOUS-TIME PROCESSES; POINT PROCESSES; ALIAS-FREE SAMPLING; ASYMPTOTIC BIAS; COVARIANCE; NORMALITY;

D O I：

10.1016/0304-4149(94)90099-X

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：

Let X = {X (t), - infinity < t < infinity} be a continuous-time stationary process with spectral density function phi(x)(lambda) and {tau(k)} be a stationary point process independent of X. Estimates ($) over cap phi(x)(lambda) of phi(x)(lambda) based on the discrete-time observation {X (tau(k)), tau(k)} are considered. Asymptotic expressions for the bias and covariance of ($) over cap phi(x)(lambda) are derived. A multivariate central limit theorem is established for the spectral estimators ($) over cap phi(x)(lambda). Under mild conditions, it is shown that the bias is independent of the statistics of the sampling point process {tau(k)} and that there exist sampling point processes such that the asymptotic variance is uniformly smaller than that of a Poisson sampling scheme for all spectral densities phi(x)(lambda) and all frequencies lambda.

引用

页码：39 / 64

页数：26