相关论文: Equivariant minimax dominators of the MLE in the a…

Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an…

We present a new version of the truncated harmonic mean estimator (THAMES) for univariate or multivariate mixture models. The estimator computes the marginal likelihood from Markov chain Monte Carlo (MCMC) samples, is consistent,…

The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the…

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…

Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…

We tackle covariance estimation in low-sample scenarios, employing a structured covariance matrix with shrinkage methods. These involve convexly combining a low-bias/high-variance empirical estimate with a biased regularization estimator,…

Analytic evaluation of heteroskedasticity consistent covariance matrix estimates (HCCME) is difficult because of the complexity of the formulae currently available. We obtain new analytic formulae for the bias of a class of estimators of…

Missing data is an important challenge when dealing with high dimensional data arranged in the form of an array. In this paper, we propose methods for estimation of the parameters of array variate normal probability model from partially…

For a multinomial distribution, suppose that we have prior knowledge of the sum of the probabilities of some categories. This allows us to construct a submodel in a full (i.e., no-restriction) model. Maximum likelihood estimation (MLE)…

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…

The variance of noise plays an important role in many change-point detection procedures and the associated inferences. Most commonly used variance estimators require strong assumptions on the true mean structure or normality of the error…

Recently, invariant risk minimization (IRM) was proposed as a promising solution to address out-of-distribution (OOD) generalization. However, it is unclear when IRM should be preferred over the widely-employed empirical risk minimization…

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…

Simple exponential smoothing is widely used in forecasting economic time series. This is because it is quick to compute and it generally delivers accurate forecasts. On the other hand, its multivariate version has received little attention…

We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs. By heuristically extending the Convex Gaussian Min-Max Theorem (CGMT) to non-Gaussian settings, we derive an asymptotic min-max…

We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Maximum regularized likelihood estimators (MRLEs) are arguably the most established class of estimators in high-dimensional statistics. In this paper, we derive guarantees for MRLEs in Kullback-Leibler divergence, a general measure of…

This paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the marginal residual terms are assumed uncorrelated and homoscedastic with possibly different standard…

Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate…