| Because the extended negativeiy dependent(END)sequence contains positive and association correlation,and is the generalization of positive and negative association random variables,the study of the limit properties and statistical inference theory of END sequence is an important topic in theory and practical application,and it is necessary to carry out research This topic mainly studies the strong consistency,r-moment order consistency,uniform strong consistency and convergence rate of the recursive density function estimation under the END sequence,and establishes the asymptotic normalityThis paper is mainly divided into four chapters.Chapter 1:This chapter mainly introduces the research background and methods of unknown density function estimation,the research status of END random sequence at home and abroad,and gives the main results of this paper.Chapter 2:Using Rosenthal ineguality of the END sequence and under appropriate conditions,we obtain the consistency,uniform strong consistency and r-order moment consistency of the kernel estimator of the unknown density function,and use R software to analyze the error of the estimator.Chapter 3:According to the inequality and property of END sequence under certain conditions,we study the uniformly strong convergence rate of the kernel estimator of recursive density function.Chapter 4:Through the properties of END sequence and its assumptions,the asymptotic normality of the kernel estimation of the recursive density function of estimator END random variables is established. |
