Related papers: An elementary analysis of ridge regression with ra…
This paper proposes an adaptive random experiment design (ARED) algorithm that can be applied to optimize the multiple factors and levels experiments. The algorithm takes real-time model error as the adaptive condition, and outputs a model…
By using the framework of Determinantal Point Processes (DPPs), some theoretical results concerning the interplay between diversity and regularization can be obtained. In this paper we show that sampling subsets with kDPPs results in…
Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine…
Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the…
This article provides an introduction to the Regression Discontinuity (RD) design, and its application to empirical research in the medical sciences. While the main focus of this article is on causal interpretation, key concepts of…
We discuss estimation and inference of conditional treatment effects in regression discontinuity (RD) designs with multiple scores. In addition to local linear regressions and the minimax-optimal estimator more recently proposed by Imbens…
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…
It is common practice to incorporate additional covariates in empirical economics. In the context of Regression Discontinuity (RD) designs, covariate adjustment plays multiple roles, making it essential to understand its impact on analysis…
We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size,…
Ridge regression is a popular method for dense least squares regularization. In this work, ridge regression is studied in the context of VAR model estimation and inference. The implications of anisotropic penalization are discussed and a…
Selective prediction, where a model has the option to abstain from making a decision, is crucial for machine learning applications in which mistakes are costly. In this work, we focus on distributional regression and introduce a framework…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
The Kaczmarz and Gauss-Seidel methods aim to solve a linear $m \times n$ system $\boldsymbol{X} \boldsymbol{\beta} = \boldsymbol{y}$ by iteratively refining the solution estimate; the former uses random rows of $\boldsymbol{X}$ {to update…
Many statistical problems can be reduced to a linear inverse problem in which only a noisy version of the operator is available. Particular examples include random design regression, deconvolution problem, instrumental variable regression,…
Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
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…
Ridge regression is a well established regression estimator which can conveniently be adapted for classification problems. One compelling reason is probably the fact that ridge regression emits a closed-form solution thereby facilitating…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
This paper analyzes the possibilities of using the generalized ridge regression to mitigate multicollinearity in a multiple linear regression model. For this purpose, we obtain the expressions for the estimated variance, the coefficient of…