Asymptotic behavior of maximum likelihood estimates of superimposed exponential signals

Abstract

Strong consistency and asymptotic normality are derived for the maximum-likelihood estimates (MLEs) of the unknown parameters ( omega /sub 1/,. . ., omega /sub p/), ( alpha /sub 1/,. . ., alpha /sub p/), and sigma /sup 2/ in the superimposed exponential model for signals, Y/sub t/= Sigma alpha exp (it omega /sub k/)+e/sub t/, where the summation is from k=1 to p, t=0, 1, . . ., n-1, and sigma /sup 2/ is the variance of the complex normal distribution of e/sub t/. As a by-product, it is found that the MLEs of the parameters attain the Cramer-Rao lower bound for the asymptotic covariance matrix. >