Related papers: Linear regression under model uncertainty

Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…

This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information is unknown and can depend on both predictors and…

Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…

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…

Model uncertainty is a crucial issue in statistics, econometrics and machine learning, yet its definition remains ambiguous and is subject to various interpretations in the literature. So far, there has not been a universally accepted…

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…

Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the…

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…

Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…

The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…

The interpretation of coefficients from multivariate linear regression relies on the assumption that the conditional expectation function is linear in the variables. However, in many cases the underlying data generating process is…

We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…

This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…