A Remark on the Efficient Estimation

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概要

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• In the classical theory of estimation, the efficiency of an unbiased estimate α^* depends on the parameter α chosen in the frequency function (fr. f.), so long as we define it as {nE(α^*-α)^2ヅ (∂ logf(x, α)/∂α)^2}^<-1> in the one parameter case. For example, in the case of the normal distribution with mean 0, and variance σ^2, there exists an efficient unbiased estimate for σ^2, but not for σ. This situation cannot be justified very well from the viewpoint where we are interested in the estimation of the distribution itself, but not of parameters. In this paper we shall give a condition to be able to choose a parameter admitting an efficient unbiased estimate, and further show the uniqueness of such a parameter under this condition. Throughout this paper the discussions will be restricted, for simplicity, to the case of one parameter and of continuous type.

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著者

• 工藤 弘吉

  Department Of Mathematics Faculty Of Science Ochanomizu University

関連論文

• On Minimax Invariant Estimates of the Transformation Parameter
• A Theorem of Kakutani on Infinite Product Measures
• A Remark on the Efficient Estimation
• On a Formulation of Classical Problems of Statistics

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