Acta mathematica scientia,Series B ›› 1989, Vol. 9 ›› Issue (4): 403-413.
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Wei Laisheng
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Abstract: Consider the two-sided truncation distribution families written in the form f(x,θ)=w(θ1, θ2)·h(x)I[θ1,θ2](x)dx, where θ=(θ1,θ2). T(X)=(t1(X), t2(X))=(min(X1, …, Xm), max(X1, …, Xm)) is a sufficient statistic and we denote its marginal density by f(t)dμT. The prior distribution of θ belong to the famlly J={G:∫∫Θ||θ||2dG(θ)<∞}. In this paper, we have constructed the empirical Bayes (EB) estimator of θ, φn(t), by using the kernel estimation of f(t) and established its convergence rates. Under suitable conditions it is shown that the rates of convergenc of EB estimator are O(N-((λk-1)(k+1))/(2(k+2)k)), where the neural number k > 1 and 1/2 < λ < 1-(1/2k). Finally an example about this result is given.
Wei Laisheng. THE CONVERGENCE RATES OF EMPIRICAL BAYES ESTIMATION FOR PARAMETERS OF TWO-SIDED TRUNCATION DISTRIBUTION FAMILIES[J].Acta mathematica scientia,Series B, 1989, 9(4): 403-413.
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