Nonparametric Estimation of Mean

This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler ( rst moment) and to the spectral width (square root of the second spectral centered moment). By assuming that the power spectral density of the underlying process is bandlimited, the maximum likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariances is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the power spectral density (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariances are unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram based estimates, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order. Refererence [1] is a short version of this work. This work was supported by Portuguese PRAXIS XXI program, under project 2/2.1.TIT/1580/95. Corresponding Author.