Constrained Maximum Likelihood Estimators for Superimposed Exponential Signals

摘要

Recently Kundu (1993a) has proposed a nonlinear eigenvalue method for finding themaximum likelihood estimators (MLE) of the parameters of undamped exponential signals. It is known to perform better than the previously existing methods like FBLP of Tufts and Kumaresan (1982) or Fisarenko's method (Pisarenko, 1972), in the sense of lower mean squared errors. The solution in general depends on the roots of a polynomial equation. It is observed that the coefficients of the polynomial exhibit a certain symmetry. Since it is known (Crowder, 1984) that the MLE with constraints is more efficient than the unconstrained MLE, modified maximum likelihood method has been suggested to estimate the parameters under these symmetric constraints. It is observed in the simulation study that the mean squared errors of the constrained MLE are closer to the Cramer-Rao lower bound than the ordinary MLE in almost all the situations.