THIRD ORDER ASYMPTOTIC PROPERTIES OF BLUE AND LSE FOR A REGRESSION MODEL WITH ARMA RESIDUAL

研究成果: Article

3 引用 (Scopus)

抄録

Abstract. In this note, we shall investigate third‐order asymptotic properties of BLUE and LSE for a regression model with ARMA residual. In the first place we shall evaluate the asymptotic mean square errors of BLUE and LSE up to third order. For appropriate regression variables (constant or harmonic functions), the asymptotic mean square error of LSE coincides with that of BLUE up to second order. Then we shall evaluate the difference of the asymptotic mean square errors of LSE and BLUE at third order. Secondly we shall show that BLUE is third‐order asymptotically efficient in the sense of the highest probability concentration around the true value in the third‐order Edgeworth expansion.

元の言語English
ページ(範囲)111-114
ページ数4
ジャーナルJournal of Time Series Analysis
8
発行部数1
DOI
出版物ステータスPublished - 1987
外部発表Yes

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Autoregressive Moving Average
Mean square error
Asymptotic Properties
Regression Model
Harmonic functions
Edgeworth Expansion
Constant function
Evaluate
Harmonic Functions
Regression
Regression model
Asymptotic properties
Autoregressive moving average

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

これを引用

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N2 - Abstract. In this note, we shall investigate third‐order asymptotic properties of BLUE and LSE for a regression model with ARMA residual. In the first place we shall evaluate the asymptotic mean square errors of BLUE and LSE up to third order. For appropriate regression variables (constant or harmonic functions), the asymptotic mean square error of LSE coincides with that of BLUE up to second order. Then we shall evaluate the difference of the asymptotic mean square errors of LSE and BLUE at third order. Secondly we shall show that BLUE is third‐order asymptotically efficient in the sense of the highest probability concentration around the true value in the third‐order Edgeworth expansion.

AB - Abstract. In this note, we shall investigate third‐order asymptotic properties of BLUE and LSE for a regression model with ARMA residual. In the first place we shall evaluate the asymptotic mean square errors of BLUE and LSE up to third order. For appropriate regression variables (constant or harmonic functions), the asymptotic mean square error of LSE coincides with that of BLUE up to second order. Then we shall evaluate the difference of the asymptotic mean square errors of LSE and BLUE at third order. Secondly we shall show that BLUE is third‐order asymptotically efficient in the sense of the highest probability concentration around the true value in the third‐order Edgeworth expansion.

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KW - third‐order asymptotic efficiency

KW - Times series regression

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