Optimal smoothing parameter of Fourier series density estimates under an autoregressive dependence model
Abstract Let f be a density possessing some smoothness properties and let X1,…, Xn be a sample from the process {Xi:|i| = 0, 1, 2,…,}, which is assumed to be strictly stationary, and assume that each Xi has a density function f. Some desirable properties of Fourier series density elements fn,λ of f of the form where f v is an estimate of fv, are discussed. A simple method for estimating λ under independence observations are considered. The mean integrated square error under an autoregressive dependence model is addressed.