When the true mixing density is known to be continuous, the maximum likelihood estimate of the mixing density does not provide a satisfying answer due to its degeneracy. Estimation of mixing densities is a well-known ill-posed indirect problem. In this article, we propose to estimate the mixing density by maximizing a penalized likelihood and call the resulting estimate the nonparametric maximu...

When the true mixing distribution is known to be continuous, the nonparametric maximum likelihood estimate of the mixing distribution cannot provide a satisfying answer due to its degeneracy. The estimation of mixing densities is an ill-posed indirect problem. In this article, we propose to estimate the mixing density by maximizing a penalized likelihood and call the resulting estimate the nonp...

Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenst...

Standard methods frequently produce zero estimates of dispersion parameters in the underlying linear mixed model. As a consequence, the EBLUP estimate of a small area mean reduces to a simple regression estimate. In this paper, we consider a class of generalized maximum residual likelihood estimators that covers the well-known profile maximum likelihood and the residual maximum likelihood estim...

Maximum parsimony and maximum likelihood are two contrasting approaches for reconstructing phylogenetic trees from sequence and character data. We establish analytic links between these methods (extending connections reported earlier) under the simple Poisson model of substitutions in two settings. First, we show that if the underlying state space is sufficiently large then the maximum likeliho...

The performance of a commonly employed linear array of sonar sensors is assessed for point-target localization. Two different methods of combining time-of-flight information from the sensors are described to estimate the range and azimuth of the target: pairwise estimate method and the maximum likelihood estimator. The biases and variances of the methods are investigated and their combined effe...

If there are many independent, identically distributed observations governed by a smooth, finite-dimensional statistical model, the Bayes estimate and the maximum likelihood estimate will be close. Furthermore, the posterior distribution of the parameter vector around the posterior mean will be close to the distribution of the maximum likelihood estimate around truth. Thus, Bayesian confidence ...

In this paper we investigate the large-sample behavior of the maximum likelihood estimate (MLE) of the unknown parameter θ for processes following the model dξt = θf(t)ξt dt+ dBt where f : R → R is a continuous function with period, say P > 0, and which is observed through continuous time interval [0, T ] as T → ∞. Here the periodic function f(·) is assumed known. We establish the consistency o...