具有测量误差的样本下连续型单参数指数族参数的经验Bayes检验

Empirical Bayes Test for the Continuous One-parameter Exponential Family with Error of Measurement

讨论了具有测量误差的样本下连续型单参数指数族参数的经验Bayes(EB)双侧检验问题.利用密度函数的逆卷积核估计构造了参数的EB检验函数,在适当的条件下证明了所提出的EB检验函数的渐近最优性,并获得了其收敛速度.

For the data with error of measurement in historical samples,the empirical Bayes(EB) two-sided test problem about the continuous one-parameter exponential family is constructed.The empirical Bayes test rule is constructed by deconvolution kernel estimation of probability density function.It is shown that the asymptotically optimal property and convergence rate for the proposed EB test rule are obtained under suitable conditions.