Related papers: On the maximum likelihood estimation in general lo…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
The principal innovative idea in this paper is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear…
Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…
In Generalized Linear Models (GLMs) it is assumed that there is a linear effect of the predictor variables on the outcome. However, this assumption is often too strict, because in many applications predictors have a nonlinear relation with…
The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…
The analysis of datasets taking the form of simple, undirected graphs continues to gain in importance across a variety of disciplines. Two choices of null model, the logistic-linear model and the implicit log-linear model, have come into…
We extend the approach in [Ann. Statist. 38 (2010) 2499-2524] for identifying locally optimal designs for nonlinear models. Conceptually the extension is relatively simple, but the consequences in terms of applications are profound. As we…
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation…
A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…
Mixture of autoregressions (MoAR) models provide a model-based approach to the clustering of time series data. The maximum likelihood (ML) estimation of MoAR models requires the evaluation of products of large numbers of densities of normal…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients,…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
In this paper, we study sample size thresholds for maximum likelihood estimation for tensor normal models. Given the model parameters and the number of samples, we determine whether, almost surely, (1) the likelihood function is bounded…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
The conditional logit model is a standard workhorse approach to estimating customers' product feature preferences using choice data. Using these models at scale, however, can result in numerical imprecision and optimization failure due to a…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies…
There have been many applications of deep neural networks to detector calibrations and a growing number of studies that propose deep generative models as automated fast detector simulators. We show that these two tasks can be unified by…