Estimation of the mean of a stationary time series by sampling

Author:

Brillinger David R.

Abstract

Let X(t), – ∞ < t < ∞, be a stationary time series with mean cx. Let 0 < τ1 < τ2 < … < τNT denote A given sampling times in the interval (0, T]. We determine the asymptotic distribution of the estimate [X1) + … + XN)]/N of cx when the sampling times are fixed, satisfying a form of generalised harmonic analysis requirement, and when the sampling times are the times of events of a stationary point process independent of the series X(t). The results obtained may be viewed as non-standard central limit theorems.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference13 articles.

1. On Stochastic Limit and Order Relationships

2. Error-Free Recovery of Signals from Irregularly Spaced Samples

3. The use of the characteristic functional and semi-invariants in the ergodic theory of stationary processes;Leonov;Soviet Math. Dokl.,1960

4. On a Method of Calculation of Semi-Invariants

5. Alias-free randomly timed sampling of stochastic processes

Cited by 42 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Estimation on unevenly spaced time series;Journal of Time Series Analysis;2023-06-15

2. One country, two systems? The heavy-tailedness of Chinese A- and H- share markets;Emerging Markets Review;2019-03

3. Local block bootstrap for inhomogeneous Poisson marked point processes;Bernoulli;2018-02-01

4. Inference with Few Heterogeneous Clusters;Review of Economics and Statistics;2016-03

5. Inference and Empirical Examples;Heavy-Tailed Distributions and Robustness in Economics and Finance;2015

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3