本文所研究之機率密度函數之估計以正交級數估計法(orthogronal series estimation),多項式鑑別法(polynanial discriminant method),置眾數機率密度之最概法(maximum likelihood estimation of a unimodal density),最短距離法(minimum distance method)為主,另外亦介紹kernel法。在正交級數法內我們利用富氏級數,legendre多項式,leguerre多項式以及hear函數推算機率密度之估計函數並附例題且證明其「一致性」此外又估計該什計函數之平均方差之級(order);另外在多頸式鑑別法我們亦證出「一致性」並加以舉例;而在最概法內亦考慮在新的條件下之估計函數;在最短距離內亦對一般短距離估計法,平均方差與kernel估計法之平均方差作一比較。
In this thesis,theprobability density estimation is investigated by using orthogonal series method,polynomial discriminant method, maximun liklihood estimation of a unimodal density,and minimum distance method.In the orthogonal series principle,the estimation is based on Fourier series,Legendre polynomial,Legendre polynomial,Leguerre polynomial,and Haar function;these estimator's consistencies are shown, and the orders of estimator's mean integrated square errors and mean square errors are investigated, and then some numerical studues is qiven. The consistent property in polynomial discriminant estimators are also shown and on example is given . An estimator in maximum likelihood estimation of a unimodal density is found. The mean square error in general nearest neighbor density estimator with kernel estimator are compared.