Nonparametric estimation of a probability density function and its derivatives. C-approach

Nonparametric (kernel) estimation of a probability density function f(x) for a sample of finite size is considered using the C-approach. The smoothness parameter β of the estimated probability density is introduced. For the case β > 2, it is shown that the convergence of the density estimate fn(x) to the function f(x) can be improved by using alternating-sign weight functions (higher-order weight functions). Estimation of the derivatives of a function is briefly considered using the same approach.