The Non-parametric Density Estimation And Its Applications To Discriminant Analysis

The nonparametric estimation of the density functionis an important directionfor modern statistics development in recently most 20 years which varies the patternof the traditional statistics development. The density function can benon-parametricly estimated through many ways, mainly by the rectangle, theRosenblatt, the Parzen kernel and the nearest neighbor.By the development of computer technology, the application that based on thenon-parametric estimation overcomes the puzzles, such as the non-parametricestimation's theory on big sample, the application based on big data and the complexoperation; begins to involve more and more fields, i.e.: social sciences, physics,biology and engineering and technique. Why the non-parametric estimation isimportant? Because it can be applied not only alone but also by the middle link ofstatistics inference, such as the non-parametric discriminant analysis, assembleanalysis and imitating random figure.According to the index of four aspects(payoff ability, refund ability,developmental ability, finance level) of a company coming into the market, theestimation to its financial status in the securities business is very important to theinterest group, especially to the most investors by judging whether the loss will STand NST.This paper detailedly introduce kernel of probability density, big-sample theroyof nearest neighboring estimate, academic basis of nonparameteric discriminance andprinciple of nonparameteric discriminance which bases on kernel and neighboringestimate, and it also present a statistical software program of the nonparametermethod. Finally, this text uses the nonpararneter method to set up a financial anticipatorysystem. This method explains the nonparametric density estimation is very appliedand conformable in the discriminant analysis. Through the comparison of the twomethods by computing and analysing, this article indirectly compares thecharacteristics and merits of the non-parametric kernel density estimation and thenon-parametric nearest neighbor estimate.