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This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…

Methodology · Statistics 2026-05-21 Jiehan Liu , Ziyi Liu , Yiqing Xu

Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…

Statistics Theory · Mathematics 2008-12-18 Sam Efromovich

Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…

Methodology · Statistics 2023-11-14 Jana Kleinemeier , Nadja Klein

Nonparametric random coefficient (RC)-density estimation has mostly been considered in the marginal density case under strict independence of RCs and covariates. This paper deals with the estimation of RC-densities conditional on a…

Econometrics · Economics 2022-01-21 Stephan Martin

We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate.…

Numerical Analysis · Mathematics 2023-08-14 Vinh Hoang , Luis Espath , Sebastian Krumscheid , Raúl Tempone

A two-stage batch estimation algorithm for solving a class of nonlinear, static parameter estimation problems that appear in aerospace engineering applications is proposed. It is shown how these problems can be recast into a form suitable…

Signal Processing · Electrical Eng. & Systems 2020-02-18 Kerry Sun , Demoz Gebre-Egziabher

We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based…

Methodology · Statistics 2019-05-03 Sanjay Chaudhuri , Mark S. Handcock

In this paper, we apply doubly robust approach to estimate, when some covariates are given, the conditional average treatment effect under parametric, semiparametric and nonparametric structure of the nuisance propensity score and outcome…

Statistics Theory · Mathematics 2020-09-15 Chuyun Ye , Keli Guo , Lixing Zhu

While much of the causal inference literature has focused on addressing internal validity biases, both internal and external validity are necessary for unbiased estimates in a target population of interest. However, few generalizability…

Methodology · Statistics 2023-04-07 Irina Degtiar , Tim Layton , Jacob Wallace , Sherri Rose

Plausible identification of conditional average treatment effects (CATEs) may rely on controlling for a large number of variables to account for confounding factors. In these high-dimensional settings, estimation of the CATE requires…

Econometrics · Economics 2023-01-18 Adam Baybutt , Manu Navjeevan

We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding…

Methodology · Statistics 2014-12-02 Peter Bühlmann , Jonas Peters , Jan Ernest

For randomized clinical trials where a single, primary, binary endpoint would require unfeasibly large sample sizes, composite endpoints are widely chosen as the primary endpoint. Despite being commonly used, composite endpoints entail…

Methodology · Statistics 2022-09-27 Marta Bofill Roig , Guadalupe Gómez Melis , Martin Posch , Franz Koenig

Numerous variable selection methods rely on a two-stage procedure, where a sparsity-inducing penalty is used in the first stage to predict the support, which is then conveyed to the second stage for estimation or inference purposes. In this…

Applications · Statistics 2015-05-28 Jean-Michel Bécu , Yves Grandvalet , Christophe Ambroise , Cyril Dalmasso

A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function…

Statistics Theory · Mathematics 2024-03-26 Masayo Y. Hirose , Shuhei Mano

The determination of the sample size required by a crossover trial typically depends on the specification of one or more variance components. Uncertainty about the value of these parameters at the design stage means that there is often a…

Methodology · Statistics 2018-03-28 Michael Grayling , Adrian Mander , James Wason

Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they…

Econometrics · Economics 2025-09-17 Timothy B. Armstrong , Patrick Kline , Liyang Sun

Quantile regression is a powerful tool for detecting exposure-outcome associations given covariates across different parts of the outcome's distribution, but has two major limitations when the aim is to infer the effect of an exposure.…

We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there…

Applications · Statistics 2016-12-05 Isaiah Andrews , Timothy B. Armstrong

In clinical trials, inferences on clinical outcomes are often made conditional on specific selective processes. For instance, only when a treatment demonstrates a significant effect on the primary outcome, further analysis is conducted to…

Methodology · Statistics 2025-04-15 Tianyu Pan , Vivek Charu , Ying Lu , Lu Tian

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

Statistics Theory · Mathematics 2020-07-20 Matias D. Cattaneo , Max H. Farrell , Yingjie Feng
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