Related papers: Optimized Regression Discontinuity Designs
Given n experiment subjects with potentially heterogeneous covariates and two possible treatments, namely active treatment and control, this paper addresses the fundamental question of determining the optimal accuracy in estimating the…
Regression discontinuity (RD) designs are popular quasi-experimental studies in which treatment assignment depends on whether the value of a running variable exceeds a cutoff. RD designs are increasingly popular in educational applications…
A popular technique for selecting and tuning machine learning estimators is cross-validation. Cross-validation evaluates overall model fit, usually in terms of predictive accuracy. In causal inference, the optimal choice of estimator…
In various statistical settings, the goal is to estimate a function which is restricted by the statistical model only through a conditional moment restriction. Prominent examples include the nonparametric instrumental variable framework for…
In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a…
The assessment of regression models with discrete outcomes is challenging and has many fundamental issues. With discrete outcomes, standard regression model assessment tools such as Pearson and deviance residuals do not follow the…
Regression discontinuity design (RDD) is widely adopted for causal inference under intervention determined by a continuous variable. While one is interested in treatment effect heterogeneity by subgroups in many applications, RDD typically…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient…
Response-biased sampling, in which samples are drawn from a popula- tion according to the values of the response variable, is common in biomedical, epidemiological, economic and social studies. In particular, the complete obser- vations in…
We propose a way of transforming the problem of conditional density estimation into a single nonparametric regression task via the introduction of auxiliary samples. This allows leveraging regression methods that work well in high…
The boundary discontinuity (BD) design is a non-experimental method for identifying causal effects that exploits a thresholding rule based on a bivariate score and a boundary curve. This widely used method generalizes the univariate…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
We consider T-optimal experiment design problems for discriminating multi-factor polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets.…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each…
We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…