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A pair of estimating equations for a mean vector

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  • Yanagimoto, Takemi

Abstract

Consider a class of estimators of a mean vector, indexed by a parameter. We introduce a pair of estimating equations for the parameter and the variance in the normal distribution. The equations provide us with an interpretation of the empirical Bayes method for smoothing and the James-Stein estimator. They can also be applied to various methods such as the S function lowess, the ridge estimator and the method of moving average. An extension to the non-Gaussian case is also discussed.

Suggested Citation

  • Yanagimoto, Takemi, 2000. "A pair of estimating equations for a mean vector," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 97-103, October.
    • Handle: RePEc:eee:stapro:v:50:y:2000:i:1:p:97-103
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    References listed on IDEAS

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    1. Takemi Yanagimoto, 1994. "The Kullback-Leibler risk of the Stein estimator and the conditional MLE," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 29-41, March.
    2. Shiller, Robert J, 1973. "A Distributed Lag Estimator Derived from Smoothness Priors," Econometrica, Econometric Society, vol. 41(4), pages 775-788, July.
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