Metrika (2008) 68:271–288 DOI 10.1007/s00184-007-0157-0 Estimating a restricted normal mean Somesh Kumar · Yogesh Mani Tripathi Received: 27 December 2005 / Published online: 12 December 2007 © Springer-Verlag 2007 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 ¯ 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. Keywords Maximum likelihood estimator · Rao-Blackwellization · Bayes estimator · Minimaxity · Equivariant estimator · Admissibility 1 Introduction In many estimation problems, the unknown parameter of interest is often bounded. Physical aspects of the experiment quite often lead to some a priori information about the parameter to be estimated. The average per capita income of a developing coun- try is likely to lie between those of an underdeveloped and a developed country. The average fuel efficiency of a new model of passenger car will lie between those of S. Kumar (B ) · Y. M. Tripathi Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721 302, India e-mail: smsh@iitkgp.ac.in Y. M. Tripathi e-mail: yogesh@maths.iitkgp.ernet.in 123