Related papers: Maximum likelihood estimation in log-linear models
We extend the constrained maximum likelihood estimation theory for parameters of a completely identified model, proposed by Aitchison and Silvey (1958), to parameters arising from a partially identified model. With a partially identified…
Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…
In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum…
The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to…
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC) distributions.…
The idea of maximizing the likelihood of the observed range for a set of jointly realized counts has been employed in a variety of contexts. The applicability of the MLE introduced in [1] has been extended to the general case of a…
Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
We consider a linear model which can have a large number of explanatory variables, the errors with an asymmetric distribution or some values of the explained variable are missing at random. In order to take in account these several…
Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…
Consider an $(L,1)$ random walk in an i.i.d. random environment, whose environment involves certain parameter. We get the maximum likelihood estimator(MLE) of the environment parameter which can be written as functionals of a multitype…
The restricted maximum likelihood method enhances popularity of maximum likelihood methods for variance component analysis on large scale unbalanced data. As the high throughput biological data sets and the emerged science on uncertainty…
In this paper we consider Poisson loglinear models with linear constraints (LMLC) on the expected table counts. Multinomial and product multinomial loglinear models can be obtained by considering that some marginal totals (linear…
We import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation produces a perturbation of sample data, which we call a…
Subsampling is a computationally effective approach to extract information from massive data sets when computing resources are limited. After a subsample is taken from the full data, most available methods use an inverse probability…
We consider a one-dimensional recurrent random walk in random environment (RWRE) when the environment is i.i.d. with a parametric, finitely supported distribution. Based on a single observation of the path, we provide a maximum likelihood…
This paper deals with a parametrized family of partially observed bivariate Markov chains. We establish that, under very mild assumptions, the limit of the normalized log-likelihood function is maximized when the parameters belong to the…
In this letter, we revisit the problem of maximum likelihood estimation (MLE) of parameters of Gaussian Mixture Model (GMM) and show a new derivation for its parameters. The new derivation, unlike the classical approach employing the…