Likelihood Estimator Of Mean Research Articles

Mean likelihood frequency estimation

Estimation of signals with nonlinear as well as linear parameters in noise is studied. Maximum likelihood estimation has been shown to perform the best among all the methods. In such problems, joint maximum likelihood estimation of the unknown parameters reduces to a separable optimization problem, where first, the nonlinear parameters are estimated via a grid search, and then, the nonlinear parameter estimates are used to estimate the linear parameters. We show that a grid search can be avoided by using the mean likelihood estimator for estimating the unknown nonlinear parameters and how its performance can be made equivalent to that of the maximum likelihood estimator (MLE). The mean likelihood estimator requires computation of a multidimensional integral. However, using the concepts of importance sampling, we obtain the mean likelihood estimate without using integration. The technique is computationally far less burdensome than the direct maximum likelihood method but performs just as well. Simulation examples for estimating frequencies of multiple sinusoids in noise are given. The general technique can be applied to a large class of nonlinear regression problems.

On mean scaled insurance risk models

A characterization problem for scale compound parametric families of distributions with the mean as scale parameter is analyzed. If the counting distribution of the compound family has the sample mean as maximum likelihood estimator of the counting mean, and if the maximum likelihood estimator of the mean scale parameter is the sample mean, then the compound family has necessarily a gamma secondary distribution. Necessary and sufficient conditions under which such a characterization holds are derived. Among the rich class of counting statistical models, which lead to such a characterization, one finds the Poisson, binomial, negative binomial, Hermite, Delaporte, extended Poisson-Pascal, mixed Poisson inverse Gaussian, Sichel, generalized Euler, and many others. The mixed Poisson lognormal is a counterexample for which the present characterization fails.

The maximum likelihood estimators in a multivariate normal distribution with AR(1) covariance structure for monotone data

The maximum likelihood estimators are uniquely obtained in a multivariate normal distribution with AR(1) covariance structure for monotone data. The maximum likelihood estimator of mean is unbiased.