Related papers: Weighted sampling, Maximum Likelihood and minimum …
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…
This paper extends the empirical minimum divergence approach for models which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to…
We study minimax convergence rates of nonparametric density estimation in the Huber contamination model, in which a proportion of the data comes from an unknown outlier distribution. We provide the first results for this problem under a…
We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based…
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…
The Rasch model, a classical model in the item response theory, is widely used in psychometrics to model the relationship between individuals' latent traits and their binary responses to assessments or questionnaires. In this paper, we…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
Consider the mean-field spin models where the Gibbs measure of each configuration depends only on its magnetization. Based on the Stein and Laplace methods, we give a new and short proof for the scaling limit theorems with convergence rate…
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum…
This paper studies the expected $L_p$-discrepancy ($2 \leq p < \infty$) for stratified sampling schemes under importance sampling. We introduce a parametric family of equivolume partitions $\Omega_{\theta,\sim}$ and leverage recent exact…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and…
A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…
A significant hurdle for analyzing large sample data is the lack of effective statistical computing and inference methods. An emerging powerful approach for analyzing large sample data is subsampling, by which one takes a random subsample…
We investigate the problem of semi-parametric maximum likelihood under constraints on summary statistics. Such a procedure results in a discrete probability distribution that maximises the likelihood among all such distributions under the…
We consider a one dimensional sub-ballistic random walk evolving in a parametric i.i.d. random environment. We study the asymptotic properties of the maximum likelihood estimator (MLE) of the parameter based on a single observation of the…
In this paper, we compare maximum likelihood (ML), quasi likelihood (QL) and weighted least squares (WLS) estimators for proportional error nonlinear regression models. Literature on thermoluminescence sedimentary dating revealed another…
A new family of minimum distance estimators for binary logistic regression models based on $\phi$-divergence measures is introduced. The so called "pseudo minimum phi-divergence estimator"(PM$\phi$E) family is presented as an extension of…