This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T ). An inferential theory is developed. We establish not only consistency but also the rate of convergence and the limiting distributions. Five different sets of identification conditions are considered....

We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, i.e. a density of the form f(0) = exp varphi(0) where varphi(0) is a concave function on R. Existence, form, characterizations and uniform rates of convergence of the MLE are given by Rufibach (2006) and Dümbgen and Rufibach (2007). The characterization of the log-concave MLE in term...

Abstract In this paper, the estimation of R=Pr(Y < Y), when X and Y are two generalized inverted exponential distributions with different parameters is considered. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. Exact and asymptotic confidence intervals of R are constructed using both exact and asymptotic distributions. Assuming that the common scale pa...

The Maximum Likelihood Estimator (MLE) has commonly been used to estimate the unknown parameters in the finite mixture of distributions via the expectationmaximization (EM) algorithm. However, the MLE can be very sensitive to outliers in the data. Various approaches that have incorporated robustness in fitting mixtures and clustering are discussed. Special attention is given to the Weighted Tri...

This paper concerns the issue of the maximum-likelihood estimation (MLE) for the concentration parameters of the von Mises-Fisher (vMF) distributions, which are crucial to directional data analysis. In particular, we study the numerical approximation approach for solving the implicit nonlinear equation arising from building the MLE of the concentration parameter κ of vMF distributions. In addit...

We describe a novel algorithm called k-Maximum Likelihood Estimator (k-MLE) for learning finite statistical mixtures of exponential families relying on Hartigan’s k-means swap clustering method. To illustrate this versatile Hartigan k-MLE technique, we consider the exponential family of Wishart distributions and show how to learn their mixtures. First, given a set of symmetric positive definite...

The maximum likelihood estimators (MLEs) for the clock phase offset assuming a two-way message exchange mechanism between the nodes of a wireless sensor network were recently derived assuming Gaussian and exponential network delays. However, the MLE performs poorly in the presence of non-Gaussian or nonexponential network delay distributions. Currently, there is a need to develop clock synchron...

This paper examines necessary and sufficient conditions for the existence of Maximum Likelihood Estimates (MLE) and the propriety of the posterior under a bounded improper prior density for a wide class of discrete (or multinomial) choice models. The choice models are based on the principle of utility maximization. Our results cover a wide class of latent variable distributions defining the uti...

The existing methods for fitting mixture regression models assume a normal distribution for error and then estimate the regression parameters by the maximum likelihood estimate (MLE). In this article, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to es...

We study the behavior of the (nonparametric) maximum likelihood estimator (MLE) for bivariate censored data. The motivation for doing this was triggered by our interest in the problem of estimating the incubation time distribution of HIV/AIDS. We study the computational and algorithmic aspects of the MLE for bivariate interval censored data, and introduce an algorithm for computing the MLE whic...