Discriminant Analysis Based On Nonparametric Statistics

The probability density function is one of important concepts in statistics. The nonparametric estimation of the density functions is an important direction of the development of the modern statistics.The probability density function estimation is the technology of estimation for the unknown probability denstity function based on the observed data that can make the mean integrated square error between the true densisty and the estimated density reach the minimum.The denstity function can be nonparametricly estimated through many ways,mainly by the rectangle,the Parzen kernel and the nearest neighbor estimation.The classical nonparameter estimation method is Parzen kernel method.By the development of computer technology,the application that based on the nonparametric estimation begins to invole more and more fileds,such as the social sciences,biology,physics and engineering and technique.It can be applied by the middle link of statistics inference,such as the nonparametric discriminant analysis,assemble analysis.Discriminant analysis is a statistical method that can be widely applied in the mumultivariate statistical analysis.It refers to a statistical analysis of determining the class of the target object in the case of know classify types, based on the characteristics of various property values.Discriminant analysis process is to construct the classifying model based on a certain classification theory,to learn the classification rules from tuples of historical data and to classify the unknown tuple.This article detailed introduces the basic theory of kernel estimation and nearest neighbor estimation and principle of nonparametric discriminance which bases on kernel and neighboring estimate.Finally,this article uses the nonparametric discriminant method to discriminate main river water quality criterion.It well illustrates the nonparametric density estimation in the discriminant analysis of the practicability and applicability. By comparing two methods of calculation and analysis, this article indirectly compares the characteritics and metris of the nonparametric kernel density estimation and the nonparametric nearest neighbor estimate.