On The Research Of The Asymptotic Property Of The Density Function Estimation Under Pairwises Negative Quadrant Dependent Samples

This paper is mainly concerned with the density function estimation problems under pairwises NQD samples, based on which we got the consistency, asymptotic property as well as the consistency rates and other large sample properties of the nearest neighbor estimation and kernel estimation. All the studies together have promoted the concerned results in i.i.d case and other associationsThis paper consists of four parts.In the first section, we introduced some background information, significance, the way of density function estimation and the chief results of this paper.In the second section, we introduced the consistency of nearest neighbor density estimation under pairwises NQD samples. In addition, we also discussed its consistency rates.In the third section, we focused our attention on the density kernel estimation under pairwises NQD samples and mainly talked about its strong consistency, uniformly strong consistency and the consistency in r-th order mean.In the last section, we investigated the asymptotic normality of density function kernel estimation under pairwises NQD samples.