Minimax estimation of a bounded normal mean vector
نویسندگان
چکیده
منابع مشابه
On minimax estimation of a sparse normal mean vector
Mallows has conjectured that among distributions which are Gaussian but for occasional contamination by additive noise, the one having least Fisher information has (two-sided) geometric contamination. A very similar problem arises in estimation of a non-negative vector parameter in Gaussian white noise when it is known also that most, i.e. (1 − ǫ), components are zero. We provide a partial asym...
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K E Y W O R D S AND PHRASES Minimax decision rule; squared error loss; Dirichlet process; compact sets; Bayes rules; isotonic regression. l . INTRODUCTION In an often cited paper, BOHLMANN (1976) has considered linear minimax estimators for the mean of a univariate distribution in a nonparametr ic setting under squared error loss. To be precise, BOHLMANN assumes that Fo(x ) is a family of C D F...
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Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and Morris’ (J. Amer. Statist. Assoc. 68 (1973) 117–130) empirical Bayes approach, whereas inversely in proportion to their variances in Berger’s (Ann. Statist. 4 (1...
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Let X be a random variable from a normal distribution with unknown mean θ and known variance σ2. In many practical situations, θ is known in advance to lie in an interval, say [−m,m], for some m > 0. As the usual estimator of θ, i.e., X under the LINEX loss function is inadmissible, finding some competitors for X becomes worthwhile. The only study in the literature considered the problem of min...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1990
ISSN: 0047-259X
DOI: 10.1016/0047-259x(90)90020-i