经验过程中有关随机熵的几个结果

Some Results on Random Entropy for Empirical Processes

介绍了一般度量空间中覆盖数、包容数与度量熵的概念以及函数空间中随机距离、随机覆盖数与随机熵的概念。研究了覆盖数、包容数与随机覆盖数所满足的关系,证明了它们互相控制的几个结果。利用随机覆盖数的关系以及覆盖数与包容数之间的关系给出了以一致有界的函数族为下标集的经验过程中Evarist Gine和Joel Zinn所获得的一个有关随机熵的结果的改进形式。

The conception of the coveting numbers and the packing numbers and the metric entropy on a metric space were introduced, and the conception of the random distance and the random covering numbers and the random entropy on a function space were introduced. The rdated expressions of the covering numbers and the packing numbers and the random covering numbers were studied. Some results that controlled each other were proved. The improving form of the result on the random entropy for empirical processes indexed by uniformly bounded families of function which were obtained by Evarist Gine and Joel Zinn was given by using the relation of random covering numbers and the rdated expressions of the covering numbers and the packing numbers.