Minimax estimation for time series models

Yan Liu; Masanobu Taniguchi

doi:10.1007/s40300-021-00217-6

Minimax estimation for time series models

Yan Liu^*, Masanobu Taniguchi

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The minimax principle is very important for all the fields of statistical science. The minimax approach is to choose an estimator which protects against the largest risk possible. In this paper we show that the Whittle estimator becomes a minimax estimator for the prediction error loss. It is shown that the Whittle estimator is a Bayes estimator for Jeffreys’ prior. Because the minimax approach is very immature in time series analysis, the result shows another advantage of the Whittle estimator.

Original language	English
Journal	Metron
DOIs	https://doi.org/10.1007/s40300-021-00217-6
Publication status	Accepted/In press - 2021

Keywords

Bayes estimator
Jeffreys’ prior
Minimax estimator
Prediction error
Risk function
Vector autoregressive model
Whittle estimator

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s40300-021-00217-6

Cite this

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title = "Minimax estimation for time series models",

abstract = "The minimax principle is very important for all the fields of statistical science. The minimax approach is to choose an estimator which protects against the largest risk possible. In this paper we show that the Whittle estimator becomes a minimax estimator for the prediction error loss. It is shown that the Whittle estimator is a Bayes estimator for Jeffreys{\textquoteright} prior. Because the minimax approach is very immature in time series analysis, the result shows another advantage of the Whittle estimator.",

keywords = "Bayes estimator, Jeffreys{\textquoteright} prior, Minimax estimator, Prediction error, Risk function, Vector autoregressive model, Whittle estimator",

author = "Yan Liu and Masanobu Taniguchi",

note = "Funding Information: Taniguchi was supported by JSPS Grant-in-Aid for Scientific Research (S) 18H05290. Liu was supported by JSPS Grant-in-Aid Scientific Research (C) 20K11719. Publisher Copyright: {\textcopyright} 2021, Sapienza Universit{\`a} di Roma.",

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AU - Liu, Yan

AU - Taniguchi, Masanobu

N1 - Funding Information: Taniguchi was supported by JSPS Grant-in-Aid for Scientific Research (S) 18H05290. Liu was supported by JSPS Grant-in-Aid Scientific Research (C) 20K11719. Publisher Copyright: © 2021, Sapienza Università di Roma.

PY - 2021

Y1 - 2021

N2 - The minimax principle is very important for all the fields of statistical science. The minimax approach is to choose an estimator which protects against the largest risk possible. In this paper we show that the Whittle estimator becomes a minimax estimator for the prediction error loss. It is shown that the Whittle estimator is a Bayes estimator for Jeffreys’ prior. Because the minimax approach is very immature in time series analysis, the result shows another advantage of the Whittle estimator.

AB - The minimax principle is very important for all the fields of statistical science. The minimax approach is to choose an estimator which protects against the largest risk possible. In this paper we show that the Whittle estimator becomes a minimax estimator for the prediction error loss. It is shown that the Whittle estimator is a Bayes estimator for Jeffreys’ prior. Because the minimax approach is very immature in time series analysis, the result shows another advantage of the Whittle estimator.

KW - Bayes estimator

KW - Jeffreys’ prior

KW - Minimax estimator

KW - Prediction error

KW - Risk function

KW - Vector autoregressive model

KW - Whittle estimator

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DO - 10.1007/s40300-021-00217-6

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SN - 0026-1424

JO - Metron

JF - Metron

ER -

Minimax estimation for time series models

Abstract

Keywords

ASJC Scopus subject areas

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