Maximal deviation theory of some estimators of prior distribution functions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Maximal deviation theory of some estimators of prior distribution functions

Authors:	J Blum V Susarla

Institution:	(1) University of California-Davis, Davis, USA;(2) University of Wisconsion-Milwaukee, Milwaukee, USA;(3) Michigan State University, Michigan, USA;(4) Present address: State University of New York, New York, USA;(5) Present address: Binghamton and Michigan State University, USA

Abstract:	Summary Let $\left( {\theta _1 ,x_1 } \right), \cdots \left( {\theta _n ,x_n } \right), \cdots$ be a sequence of independent identically distributed random variables withθ ₁∼G and the conditional distribution ofx ₁ givenθ ₁=θ given by $F_{\theta _1 } \left( \cdot \right)$ . HereG is unknown andF _θ(·) is known. This paper provides estimators $\hat G_n$ ofG based onx ₁, …,x _n such that the random variable sup $\left\{ {{{\left\| {\hat G_n \left( x \right) - G\left( x \right)} \right\|} \mathord{\left/ {\vphantom {{\left\| {\hat G_n \left( x \right) - G\left( x \right)} \right\|} {c_n }}} \right. \kern-\nulldelimiterspace} {c_n }}\left( x \right)\left\| {c_1 \leqq x} \right. \leqq c_2 } \right\}$ has an asymptotic distribution asn→∞ under certain on conditionsG and for certain choices ofF _θ. A simulation model has been discussed involving the uniform distribution on (0, θ) forF _θ and an exponential distribution forG. Research supported by the National Science Foundation under Grant #MCS77-26809.

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