The Improvement And The Related Discussion Of Density Kernel Estimation

To estimate the distribution density and make statistical inference based on the sample is a nonparametric method, when the sample data distribution is unknown, or the data is seriously polluted because of various reasons. Its robustness is good and widely used. With the constant improvement of the decision reliability requirements, the in-depth study of the method has more value.First of all, the background and research significance of the kernel density estimation are summarized. For the generation and development of the kernel density estimate, a simple sum arization is made. Besides, the research idea and significance of this project is expounded.Secondly, the involved basic concept is generalized. In order to avoid the unnecessary repetition in the study of the nonparametric density estimation, the characteristics of the estim ator?()nf x is given in the form of theorem of decomposition type. Besides, the kernel estimates of the asymptotic unbiased consistency and uniform strong consistency are proved. In addition, under the condition of relatively weak, estimating the optimal rate of convergence by selecting appropriate window width are also been discussed and proved.Using polynomial fitting to improve kernel density estimation ?()nf x is the core of this paper. The deviation of decomposition ?()(?())n nf x-E f x is proved and obtained and by large sample approximation based on kernel estimation a new expression of kernel estimator?()nf x is obtained. By introducing a different set of window width, a new estimator of linear model is constructed, then, using the orthogonal approximate linear transformation makes the error of the model are independent of each other. Thus, the kernel density estimation is improved by the application of the theory of linear model. It not only can estimate the density function, but also can estimate the density function of the derivative at the same time. It reduced the esti mated workload in some extent and improved the efficiency of the estimates while keeping th e large sample properties of kernel density estimation.Finally, the asymptotic optimality of the improved kernel density estimator are discussed and proved. In order to structure inspection and do the confidence interval, a new estimator is used. At the same time, the confidence region, modal test and related problem are discussed. Furthermore, at the end of this article, a random simulation instance is made. Gaussian kernel, the appropriate window width and appropriate order polynomial are selected. For normal mix ture distribution, we make stochastic simulation for two different kinds of nuclear density esti mation through sample respectively. Based on the error MSE comparison, it show that the im proved kernel density estimator in most points fitting effect is better than the original kernel density estimator. The effectiveness of the improved method is illustrated.