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Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…

Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework…

High-dimensional prediction with multiple data types needs to account for potentially strong differences in predictive signal. Ridge regression is a simple model for high-dimensional data that has challenged the predictive performance of…

This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

A novel estimation approach for a general class of semi-parametric multivariate time series models is introduced where the conditional mean is modeled through parametric functions. The focus of the estimation is the conditional mean…

We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last $k$ terms, which are the only available values…

Estimation in exploratory factor analysis often yields estimates on the boundary of the parameter space. Such occurrences, known as Heywood cases, are characterised by non-positive variance estimates and can cause issues in numerical…

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The…

The generalized estimating equation (GEE) method is a popular tool for longitudinal data analysis. However, GEE produces biased estimates when the outcome of interest is associated with cluster size, a phenomenon known as informative…

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…

The ordinary least squares estimate in linear regression is sensitive to the influence of errors with large variance, which reduces its robustness, especially when dealing with heavy-tailed errors or outliers frequently encountered in…

Several recently developed methods have the potential to harness machine learning in the pursuit of target quantities inspired by causal inference, including inverse weighting, doubly robust estimating equations and substitution estimators…

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many…

We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

In this paper, we introduce the Generalized Mixed Regularized Reduced Rank Regression model (GMR4), an extension of the GMR3 model designed to improve performance in high-dimensional settings. GMR3 is a regression method for a mix of…

The paper considers parameter estimation in count data models using penalized likelihood methods. The motivating data consists of multiple independent count variables with a moderate sample size per variable. The data were collected during…

The statistical framework of Generalized Linear Models (GLM) can be applied to sequential problems involving categorical or ordinal rewards associated, for instance, with clicks, likes or ratings. In the example of binary rewards, logistic…