Nonparametric Estimation of a Probability Density Function and Its Derivatives. -Approach
V. G. Alekseev
Keywords: probability density function, nonparametric (kernel) estimator, uniform consistency of estimate with increasing sample size
Pages: 65-72
Abstract
Nonparametric (kernel) estimation of a probability density function f(x) for a sample of finite size is considered using the -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.
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