The Consistency Of Estimator For Probability Density Function Under M-WOD Sample

Both the recursive kernel density function estimator and the nearest neighbor density estimator are widely used density estimation methods,and their large sample properties in the case of independent samples and dependent samples have been studied by many domestic and foreign scholars.The consistency problem of density estimation has been studied by many scholars under the conditions of sequence samples such as NA,NSD,NOD,END,and WOD,and corresponding conclusions are given under different conditions.The m-WOD sequence is a very broad class of sequences including the above sequences.This paper studies the consistency of its recursive kernel density function estimator and nearest neighbor density estimator under certain conditions.This article mainly includes the following items:1.Research status of large sample properties for density estimation and existing research results of m-WOD sample;2.The mean square consistency and strong consistency of the recursive kernel density function estimator of m-WOD sample under certain conditions;3.Weak consistency and strong consistency of the nearest neighbor density estimator of m-WOD sample under certain conditions.Based on previous studies,this paper proves the probability inequalities of m-WOD sample,and generalizes the consistency of the recursive kernel density function estimator and the nearest neighbor density estimator to the m-WOD sample.