Consistency Of Recursive Kernel Estimate Of Probability Density Function Under Pairwise Positive Quadrant Dependent Sequence

The kernel estimation of density function is a very widely used nonparametric s-tatistical method.After Rosenblatt and Parzen have proposed and refined this kernel estimation,many domestic and foreign mathematical statistics scientists have studied this.Which is dependent on random variables in multiple statistical analysis,life sci-ences and many other fields have a very wide range of applications.But in practical examples of real life,the samples are often not independent of each other.So nearly 20 years,random variables of the concept of dependence and its nature of the study has aroused widespread concem.And then there have been PQD sequence,PA sequence and other positive sequence.The pairwise PQD sequence introduced in this paper is a new concept of positive dependency proposed by Lenmann in 1966,which is weaker than the PA sequence.In this paper,we study the consistency of the recursive density kernel estimation of pairwise PQD sequences.The first chapter of this paper introduces the recursive density function kernel es-timation and pairwise PQD sequence research background,the status quo at home and abroad.In the second chapter,we obtain the r-order average consistency of recursive kernel density estimation of pairwise PQD sequences.In chapter 3,we obtain the u-niformly weak consistency of recursive kernel density estimation of pairwise PQD se-quences.