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This paper considers estimation of β in the regression model y =Xβ+μ, where the error components in μ have the jointly multivariate Student-t distribution. A family of James-Stein type estimators (characterised by nonstochastic scalars) is presented. Sufficient conditions involving only X are given, under which these estimators are better (with respect to the risk under a general quadratic loss function) than the usual minimum variance unbiased estimator (MVUE) of β. Approximate expressions for the bias, the risk, the mean square error matrix and the variance-covariance matrix for the estimators in this family are obtained. A necessary and sufficient condition for the dominance of this family over MVUE is also given. 相似文献
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Practical computation of the minimum variance unbiased estimator (MVUE) is often a difficult, if not impossible, task, even
though general theory assures its existence under regularity conditions. We propose a new approach based on iterative bootstrap
bias correction of the maximum likelihood estimator to accurately approximate the MVUE. Viewing bootstrap iteration as a Markov
process, we develop a computational algorithm for bias correction based on arbitrarily many bootstrap iterations. The algorithm,
when applied parametrically to finite sample spaces, does not involve Monte Carlo simulation. For infinite sample spaces,
a nonparametric version of the algorithm is combined with a preliminary round of Monte Carlo simulation to yield an approximate
MVUE. Both algorithms are computationally more efficient and stable than conventional simulation-based bootstrap iterations.
Examples are given of both finite and infinite sample spaces to illustrate the effectiveness of our new approach.
Supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU
7026/97P). 相似文献
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Tables are given of confidence limits on tail areas, γ, of the normal distribution, where γ = P{Y ≥ L}, and where L is a given number, and Y is normally distributed with unknown mean, μ, and unknown variance, σ2. 相似文献
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Federico J. O''Reilly 《Journal of statistical planning and inference》1984,10(3):273-276
In the multivariate normal regression setting, the estimability of a distribution is studied generalizing earlier results for the univariate case. The MVUE of an estimable distribution is obtained. 相似文献
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This paper provides a simulation study which compares three estimators for R = P(Y<X) when Y and X are two independent but not identically distributed Burr random variables. These estimators are the minimum variance unbiased, the maximum likelihood and Bayes estimators. Moreover, the sensitivity of Bayes estimator to the prior parameters is considered. 相似文献
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