Bandwidth Selection in Density Estimation

The motivation for density estimation in statistics and data analysis is to realize where observations occur more frequently in a sample. The aim of density estimation is to approximate a “true” probability density function f(x) from a sample information {X _i }n_i=1 of independent and identically distributed observations. The estimated density is constructed by centering around each observation X _i a kernel function K _h (u) = K(u/h)/h with u = x - X _i , and averaging the values of this function at any given x.