Consistency Of Recursive Kernel Estimate Of Probability Density Function Under Widely Orthant Dependent Samples

The estimator problem of probability density function has always been one of the hot issue in mathematical statistics, which has always been focused by many scholars. It is well known that the limit theory of independent random variables sequences have been obtained well development, in many practical problems which the samples are not independent, but have a certain connection, after that, statiscians have proposed the concept of all kinds of dependent sequences. The class of widely orthant dependent (WOD) random variables includes independent random variables, negatively associat-ed (NA) random variables, extended negatively dependent (END) random variables as special cases. Based on the wide range of the WOD sequences, this paper researches the consistency of recursive kernel estimate of probability density function under WOD samples.In Chapter 1, we introduce some background material and the present research status at home and abroad. In Chapter 2, the strong consistency of recursive kernel estimate of probability density function under WOD samples is proved by using WOD exponential inequality under suitable conditons. In Chapter 3, the consistency in r-order mean of recursive kernel estimate of probability density function under WOD samples is studied under two different conditions.