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The Optimal Estimator of Distribution Function

Author: NingJianHui
Tutor: XieMinYu
School: Central China Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Nonparametric estimation Best invariant estimate Minimax estimation Admissible estimate
CLC: O212
Type: Master's thesis
Year: 2005
Downloads: 114
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Abstract


In this paper, we consider the sub-sample of n excellent estimate of the distribution function F given from an unknown distribution function F capacity . Symmetric loss function , the existing literature only in the case of r = 2 is given a continuous distribution function F BEST constant estimates. This article is obtained in the case of γ = 1 F BEST constant estimates. Conclusions which will be extended to the more general case , and prove that the optimal constant estimated allowable as a discrete distribution function estimates . The statistical decision due to the needs of the practical problems of asymmetric loss has been closely watched by the people . But , currently used in the discussion of non-parametric problem of asymmetric loss function literature is rare. To this end, we have introduced here and transformation parameter estimation asymmetric linear exponential loss function consider a continuous distribution function F invariant estimation problems under asymmetric loss in the under monotonic transformation group , we get F 's optimal unchanged estimates , and prove it Minimax . To enrich a the nonparametric problem in the loss of function for practitioners in this field to provide a wider choice of method and its theoretical basis .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics
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