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Estimating a restricted normal mean

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Abstract

Let X 1, X 2, ..., X n be a random sample from a normal distribution with unknown mean μ and known variance σ 2. In many practical situations, μ is known a priori to be restricted to a bounded interval, say [−m, m] for some m > 0. The sample mean \(\bar{X}\) , then, becomes an inadmissible estimator for μ. It is also not minimax with respect to the squared error loss function. Minimax and other estimators for this problem have been studied by Casella and Strawderman (Ann Stat 9:870–878, 1981), Bickel (Ann Stat 9:1301–1309, 1981) and Gatsonis et al. (Stat Prob Lett 6:21–30, 1987) etc. In this paper, we obtain some new estimators for μ. The case when the variance σ 2 is unknown is also studied and various estimators for μ are proposed. Risk performance of all estimators is numerically compared for both the cases when σ 2 may be known and unknown.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721 302, India

    Somesh Kumar & Yogesh Mani Tripathi

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  1. Somesh Kumar
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  2. Yogesh Mani Tripathi
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Correspondence to Somesh Kumar.

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Kumar, S., Tripathi, Y.M. Estimating a restricted normal mean. Metrika 68, 271–288 (2008). https://doi.org/10.1007/s00184-007-0157-0

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  • DOI: https://doi.org/10.1007/s00184-007-0157-0

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