The Large Deviation And The Medium Deviation Of The Sample Quantile Kernel Estimation Under The Dependent Sequence

Quantile is an important digital feature that can characterize the population distribu-tion.It has important theoretical and practical significance in many areas of research,such as finance,medicine,biostatistics and others.When the population quantile is unknown,we usually use the sample quantile to estimate the population quantile.But the empirical distribution function does not consider the smoothness of the population distribution,that is used to construct the sample quantile.In order to overcome this shortcoming,Nadaraya proposed the sample quantile kernel estimation in 1964,and then many scholars conduct-ed a large number of studies on the sample quantile kernel estimation.In the late 1920s,the large deviation was presented as a formal concept by Har-ald Cramer.The large and moderate deviations principle mainly describe the asymptotic properties of random variable sequences.They give the rate function,and endow it more rich connotation than the usual limit theorem.And they have been widely applied in the random disturbance,statistics,power systems,stochastic differential equations,and many other fields.In the present,there are many documents studied the large and moderate devi-ations on the independent sample sequence.However,there are many dependent samples in the practical problems.Therefore,it has the theoretical and practical significance about studing the limit properties of sample quantile kernel estimation based on the dependent sequence.In conclusion,the article will discuss the moderate and large deviations of the sample quantile kernel estimate on the m-dependent and NA sequences.It generalized some results in the independent case and expanded the application scope of sample quantile kernel estimation.The paper is divided into three chapters,the main contents are as follows:The first chapter introduces the relevant research and the significance of quantile,the large and moderate deviations and dependent sequences.Then,list the main work of this paper.The second chapter,based on the m-dependent sequences,by calculating the Cramer function and verifying the Cramer condition,the moderate and large deviations of the sample quantile kernel estimation were got.The third chapter discusses the moderate deviation of the sample quantile kermel esti-mation on the NA sequences.By using the related hypothesis,the behavior of the NA se-quence and the Markov inequality,the moderate principle of it was obtained.