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The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…

Errors-in-variables is a long-standing, difficult issue in linear regression; and progress depends in part on new identifying assumptions. I characterize measurement error as bad-leverage points and assume that fewer than half the sample…

We study a linear statistical model where outcomes depend on regressors with fixed population coefficients and observation-specific latent coefficients, along with measurement errors. A decision-maker estimates population coefficients and…

Linear regression is a frequently used tool in statistics, however, its validity and interpretability relies on strong model assumptions. While robust estimates of the coefficients' covariance extend the validity of hypothesis tests and…

Completely nonparametric transformation models with heteroscedastic errors are considered. Despite their flexibility, such models have rarely been used so far, since estimators of the model components have been missing and even…

The goodness of the long-term prediction in the state-space model was evaluated using the squared long-term prediction error. In order to estimate the model parameters suitable for long-term prediction, we devised a modified log-likelihood…

Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While many empirical studies illustrate the benefits of transfer learning, few theoretical results are…

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…

In federated learning, differences in the data or objectives between the participating nodes motivate approaches to train a personalized machine learning model for each node. One such approach is weighted averaging between a locally trained…

This paper investigates multistep prediction errors for non-stationary autoregressive processes with both model order and true parameters unknown. We give asymptotic expressions for the multistep mean squared prediction errors and…

There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…

Transfer learning refers to the promising idea of initializing model fits based on pre-training on other data. We particularly consider regression modeling settings where parameter estimates from previous data can be used as anchoring…

Increasing practical interest has been shown in regression problems where the errors, or disturbances, are centred in a way that reflects particular characteristics of the mechanism that generated the data. In economics this occurs in…

Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves…

The $k$-nearest neighbor algorithm ($k$-NN) is a widely used non-parametric method for classification and regression. We study the mean squared error of the $k$-NN estimator when $k$ is chosen by leave-one-out cross-validation (LOOCV).…

Large language models (LLMs) are increasingly used to predict human behavior. We propose a measure for evaluating how much knowledge a pretrained LLM brings to such a prediction: its equivalent sample size, defined as the amount of…

In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…

We study the nested model averaging method on the solution path for a high-dimensional linear regression problem. In particular, we propose to combine model averaging with regularized estimators (e.g., lasso and SLOPE) on the solution path…

Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…

We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…