Algorithm Of Kernel Density Estimation Of Kernel Function

In probability theory and statistics, if we can get the observed data, the probability density function estimation is the technology of estimation for the unknown probability density function. We can get the optimal bandwidth when the mean integrated square error between the true density and estimated density reach the minimum. This classical estimation method is the kernel probability density function estimation method.In actual use, it is difficult to determine the nonlinear relationship between economic variables parameters, because the econometric models usually have some differences, and can not adapt to the authentication manager and economic research. However, the best way to solve this problem is the kernel probability density function estimation. This paper firstly describes the purpose and significance of probability density function estimation method, describing the origin and development of kernel function, and analysis of the present situation of research on such topics, then selecting the appropriate kernel function or using known methods to estimate the true probability density function.Kernel probability density function estimation is nonparametric method which can be widely used in many fields, the key of kernel probability density function estimation method is the selection of kernel function and the determination of bandwidth. In this paper, we can get bandwidth of the kernel probability density function estimation method by introducing the concept of integral mean square error. Cosine kernel is used to estimate and the Solve-the-Equation method is used to derive the second derivative of the bandwidth. Finally, the iterative algorithm is designed to calaulate the optimal bandwidth. Under the premise of the determinate kernel method, cosine kernel is used to estimate unknown probability density function and make an improvement. Results show that the new kernel function improves the precision and gliding property of kernel density estimation.In statistics, consistency is one of the most basic conditions for the estimated amount. In general, if an estimator does not have the consistency, then it will not be accepted. Thus, in the last chapter, we will prove the consistency of kernel probability density function estimation and calculate its convergence rate.