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Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Variational inference is a popular method for estimating model parameters and conditional distributions in hierarchical and mixed models, which arise frequently in many settings in the health, social, and biological sciences. Variational…
A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…
We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…
The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…
Regression calibration as developed by Rosner, Spiegelman and Willet is used to correct the bias in effect estimates due to measurement error in continuous exposures. The method involves two models: a measurement error model (MEM) relating…
Estimators in statistics and machine learning must typically trade off between efficiency, having low variance for a fixed target, and distributional robustness, such as multiaccuracy, or having low bias over a range of possible targets. In…
Prediction performance does not always reflect the estimation behaviour of a method. High error in estimation may necessarily not result in high prediction error, but can lead to an unreliable prediction if test data lie in a slightly…
Logistic regression model is widely used in many studies to investigate the relationship between a binary response variable Y and a set of potential predictors $X_1,\ldots, X_p$ (for example: $Y = 1$ if the outcome occurred and $Y = 0$…
A multiple interval-valued linear regression model considering all the cross-relationships between the mids and spreads of the intervals has been introduced recently. A least-squares estimation of the regression parameters has been carried…
We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do…
In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…
This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis…
It is shown that the the popular least squares method of option pricing converges even under very general assumptions. This substantially increases the freedom of creating different implementations of the method, with varying levels of…
Utilizing covariate information has been a powerful approach to improve the efficiency and accuracy for causal inference, which support massive amount of randomized experiments run on data-driven enterprises. However, state-of-art…
Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…
Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of…
Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
Ridge regression (RR) is a regularization technique that penalizes the L2-norm of the coefficients in linear regression. One of the challenges of using RR is the need to set a hyperparameter ($\alpha$) that controls the amount of…