Related papers: The existence of maximum likelihood estimate in hi…
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However,…
We consider a model for logistic regression where only a subset of features of size $p$ is used for training a linear classifier over $n$ training samples. The classifier is obtained by running gradient descent (GD) on logistic loss. For…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
We derive uniform convergence rates for the maximum likelihood estimator and minimax lower bounds for parameter estimation in two-component location-scale Gaussian mixture models with unequal variances. We assume the mixing proportions of…
We consider maximum likelihood estimation with data from a bivariate Gaussian process with a separable exponential covariance model under fixed domain asymptotic. We first characterize the equivalence of Gaussian measures under this model.…
Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…
A powerful tool for the analysis of nonrandomized observational studies has been the potential outcomes model. Utilization of this framework allows analysts to estimate average treatment effects. This article considers the situation in…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical…
Logistic regression is widely used in many areas of knowledge. Several works compare the performance of lasso and maximum likelihood estimation in logistic regression. However, part of these works do not perform simulation studies and the…
The ability to understand and solve high-dimensional inference problems is essential for modern data science. This article examines high-dimensional inference problems through the lens of information theory and focuses on the standard…
This paper introduces a high-dimensional binary variate model that accommodates nonstationary covariates and factors, and studies their asymptotic theory. This framework encompasses scenarios where single indices are nonstationary or…
Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…
Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed in the…
Data separation is a well-studied phenomenon that can cause problems in the estimation and inference from binary response models. Complete or quasi-complete separation occurs when there is a combination of regressors in the model whose…
For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…