条件密度函数双重核估计的精确度的随机测度的收敛性

Convergence Properties of Stochastic Measures of the Accuracy of Double Kernel Estimator of Conditional Density

度量条件密度函数f(y|x)的双重核估计f_n(y|x)的精确度的量为平均积分均方误差(MISE),由于MISE的计算是十分困难的.我们采用积分均方差误A_n^(?)(ISE)和平均均方误差I_n(ASE)作为MISE的估计量,本文在一定条件下,得到A_n^(?)和I_n与MISE(=EI_n)之间的关系,即A_n^(?)=MISE+O_p(MISE)及I_n=MISE+O_p(MISE).

Sun[6] has obtained the double kernel estimator of conditional density be tbe stochastic measures of the accuracy of fn(y|x), where w is a weight function. P.Hall [3] pointed out that it is difficult to compute MISE. In this paper by using of An or In as the estimator of MISE, we obtain