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We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…

We give examples of data-generating models under which Breiman's random forest may be extremely slow to converge to the optimal predictor or even fail to be consistent. The evidence provided for these properties is based on mostly intuitive…

The incorporation of unlabeled data in regression and classification analysis is an increasing focus of the applied statistics and machine learning literatures, with a number of recent examples demonstrating the potential for unlabeled data…

Models allowing for random heterogeneity, such as mixed logit and latent class, are generally observed to obtain superior model fit and yield detailed insights into unobserved preference heterogeneity. Using theoretical arguments and two…

In most circumstances, probability sampling is the only way to ensure unbiased inference about population quantities where a complete census is not possible. As we enter the era of 'big data', however, nonprobability samples, whose sampling…

Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…

Variable selection in sparse regression models is an important task as applications ranging from biomedical research to econometrics have shown. Especially for higher dimensional regression problems, for which the link function between…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…

Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to 'mine' variables of interest…

Analysis of sample survey data often requires adjustments to account for missing data in the outcome variables of principal interest. Standard adjustment methods based on item imputation or on propensity weighting factors rely heavily on…

In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

Two-phase outcome dependent sampling (ODS) is widely used in many fields, especially when certain covariates are expensive and/or difficult to measure. For two-phase ODS, the conditional maximum likelihood (CML) method is very attractive…

Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…

According to Hansen, Madow and Tepping [J. Amer. Statist. Assoc. 78 (1983) 776--793], "Probability sampling designs and randomization inference are widely accepted as the standard approach in sample surveys." In this article, reasons are…

Standard selection criteria for forecasting models focus on information that is calculated for each series independently, disregarding the general tendencies and performances of the candidate models. In this paper, we propose a new way to…

For binary experimental data, we discuss randomization-based inferential procedures that do not need to invoke any modeling assumptions. We also introduce methods for likelihood and Bayesian inference based solely on the physical…