On flat-top kernel spectral density estimators for homogeneous random fields

The problem of nonparametric estimation of the spectral density function of a partially observed homogeneous random field is addressed. In particular, a class of estimators with favorable asymptotic performance (bias, variance, rate of convergence) is proposed. The proposed estimators are actually shown to be √N-consistent if the autocovariance function of the random field is supported on a compact set, and close to √N-consistent if the autocovariance function decays to zero sufficiently fast for increasing lags.