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An iterative feasible minimum mean squared error estimator of the disturbance variance in linear regression under asymmetric loss

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  • Wan, Alan T. K.
  • Kurumai, Hiroko

Abstract

In this article, we consider the risk performance of an iterative feasible minimum mean squared error estimator of the regression disturbance variance under the LINEX loss function. This loss is a generalisation of the quadratic loss function allowing for asymmetry. Notwithstanding the justification for using the feasible minimum mean squared error estimator in estimating the regression coefficients, it is found that the corresponding estimator of the disturbance variance does not, in general, improve over a class of conventional estimators commonly used in practice.

Suggested Citation

  • Wan, Alan T. K. & Kurumai, Hiroko, 1999. "An iterative feasible minimum mean squared error estimator of the disturbance variance in linear regression under asymmetric loss," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 253-259, November.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:3:p:253-259
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    References listed on IDEAS

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    1. Alan Wan & Anoop Chaturvedi, 2000. "Operational Variants of the Minimum Mean Squared Error Estimator in Linear Regression Models with Non-Spherical Disturbances," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 332-342, June.
    2. Michael Cain & Christian Janssen, 1995. "Real estate price prediction under asymmetric loss," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 401-414, September.
    3. Ohtani, Kazuhiro, 1987. "Inadmissibility of the iterative Stein-rule estimator of the disturbance variance in a linear regression," Economics Letters, Elsevier, vol. 24(1), pages 51-55.
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    Cited by:

    1. Fikri Akdeniz, 2004. "New biased estimators under the LINEX loss function," Statistical Papers, Springer, vol. 45(2), pages 175-190, April.
    2. Ohtani, Kazuhiro, 2001. "MSE dominance of the pre-test iterative variance estimator over the iterative variance estimator in regression," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 331-340, October.
    3. Wan, Alan T. K. & Zou, Guohua & Lee, Andy H., 2000. "Minimax and [Gamma]-minimax estimation for the Poisson distribution under LINEX loss when the parameter space is restricted," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 23-32, October.
    4. Qin, Huaizhen & Ouyang, Weiwei, 2016. "Asymmetric risk of the Stein variance estimator under a misspecified linear regression model," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 94-100.

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