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GARCH models are useful tools in the investigation of phenomena, where volatility changes are prominent features, like most financial data. The parameter estimation via quasi maximum likelihood (QMLE) and its properties are by now well…
Statistical machine learning theory often tries to give generalization guarantees of machine learning models. Those models naturally underlie some fluctuation, as they are based on a data sample. If we were unlucky, and gathered a sample…
For high-dimensional linear regression models, we review and compare several estimators of variances $\tau^2$ and $\sigma^2$ of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty…
This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…
In the missing data literature, the Maximum Likelihood Estimator (MLE) is celebrated for its ignorability property under missing at random (MAR) data. However, its sensitivity to misspecification of the (complete) data model, even under…
Missing data is a common issue in many biomedical studies. Under a paired design, some subjects may have missing values in either one or both of the conditions due to loss of follow-up, insufficient biological samples, etc. Such partially…
Originally introduced as a neural network for ensemble learning, mixture of experts (MoE) has recently become a fundamental building block of highly successful modern deep neural networks for heterogeneous data analysis in several…
Exact MLE for generalized linear mixed models (GLMMs) is a long-standing problem unsolved until today. The proposed research solves the problem. In this problem, the main difficulty is caused by intractable integrals in the likelihood…
In regression models for spatial data, it is often assumed that the marginal effects of covariates on the response are constant over space. In practice, this assumption might often be questionable. In this article, we show how a Gaussian…
Latent variable models have been widely applied in different fields of research in which the constructs of interest are not directly observable, so that one or more latent variables are required to reduce the complexity of the data. In…
Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…
Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…
Quantifying the heterogeneity of treatment effect is important for understanding how a commercial product or medical treatment affects different population subgroups. While much of treatment effect heterogeneity analysis focuses on the…
Histogram-based empirical Bayes methods developed for analyzing data for large numbers of genes, SNPs, or other biological features tend to have large biases when applied to data with a smaller number of features such as genes with…
In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number of samples needed to achieve (almost surely) three…
Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data. From multidimensional scaling to the imputation of missing data, PPCA has a broad spectrum of…
Maximum likelihood quantum state tomography yields estimators that are consistent, provided that the likelihood model is correct, but the maximum likelihood estimators may have bias for any finite data set. The bias of an estimator is the…
Maximum likelihood estimation in nonlinear models can exhibit substantial instability in finite samples when the data provide limited information about certain parameters. Such instability is driven by rare but extreme realizations of the…
The standard paradigm of neural language generation adopts maximum likelihood estimation (MLE) as the optimizing method. From a distributional view, MLE in fact minimizes the Kullback-Leibler divergence (KLD) between the distribution of the…
A connection between the General Linear Model (GLM) in combination with classical statistical inference and the machine learning (MLE)-based inference is described in this paper. Firstly, the estimation of the GLM parameters is expressed as…