Cubical and Spherical Estimation of Multivariate Probability Density
多元概率密度的立方体与球形估计
Two estimates of the density function f(x,y) of points in a plane are defined from a sample of n points by (1) counting how many points lie within a square of side 2h and center at (x,y), and (2) by counting how many points lie within a circle of diameter 2R and center at (x,y). Optimal values of h and R are shown to exist. This is done by expressing the principal part of the mean square errors of these estimates as the sum of two terms, an “error” and a “bias.” The error…