Non-asymptotic confidence estimation of the autoregressive parameter in AR(1) process with an unknown noise variance

Abstract

The paper considers the estimation problem of the autoregressive parameter in the first-order autoregressive process with Gaussian noises when the noise variance is un-known. We propose a non-asymptotic technique to compensate the unknown variance, and then, to construct a point estimator with any prescribed mean square accuracy. Also a fixed-width confidence interval with any prescribed coverage accuracy is proposed. The results of Monte-Carlo simulations are given.

Original language	English
Pages (from-to)	19-26
Number of pages	8
Journal	Austrian Journal of Statistics
Volume	49
Issue number	4
DOIs	https://doi.org/10.17713/ajs.v49i4.1121
Publication status	Published - 14 Apr 2020

Keywords

Autoregressive process
Confidence interval
Non-asymptotic estimation

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.17713/ajs.v49i4.1121

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title = "Non-asymptotic confidence estimation of the autoregressive parameter in AR(1) process with an unknown noise variance",

abstract = "The paper considers the estimation problem of the autoregressive parameter in the first-order autoregressive process with Gaussian noises when the noise variance is un-known. We propose a non-asymptotic technique to compensate the unknown variance, and then, to construct a point estimator with any prescribed mean square accuracy. Also a fixed-width confidence interval with any prescribed coverage accuracy is proposed. The results of Monte-Carlo simulations are given.",

keywords = "Autoregressive process, Confidence interval, Non-asymptotic estimation",

author = "Vorobeychikov, {Sergey E.} and Burkatovskaya, {Yulia B.}",

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AU - Burkatovskaya, Yulia B.

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AB - The paper considers the estimation problem of the autoregressive parameter in the first-order autoregressive process with Gaussian noises when the noise variance is un-known. We propose a non-asymptotic technique to compensate the unknown variance, and then, to construct a point estimator with any prescribed mean square accuracy. Also a fixed-width confidence interval with any prescribed coverage accuracy is proposed. The results of Monte-Carlo simulations are given.

KW - Autoregressive process

KW - Confidence interval

KW - Non-asymptotic estimation

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