The Estimation of Probability Densities and Cumulatives by Fourier Series Methods
用傅里叶级数估计概率密度与累积分布
A class of estimators (referred to as the Fourier estimators m and m) of the probability density function f and the associated cumulative distribution function F are considered. Here m = Σmk=0 âkψk and m = Σmk=0 Âk ψk where the functions {ψk} comprise an orthogonal set with respect to weight function w(x), and the statistics âk and Âk are formed from the n unordered observations.Simple expressions are found for the mean integrated square errors, M.I.S.E., of the estimators m…