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There are many nonparametric objects of interest that are a function of a conditional distribution. One important example is an average treatment effect conditional on a subset of covariates. Many of these objects have a conditional…

Statistics Theory · Mathematics 2024-12-25 Victor Chernozhukov , Whitney K. Newey , Vasilis Syrgkanis

The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…

Methodology · Statistics 2021-01-01 Sjoerd Viktor Beentjes , Ava Khamseh

Nonlinearity and endogeneity are prevalent challenges in causal analysis using observational data. This paper proposes an inference procedure for a nonlinear and endogenous marginal effect function, defined as the derivative of the…

Econometrics · Economics 2024-06-19 Qingliang Fan , Zijian Guo , Ziwei Mei , Cun-Hui Zhang

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…

Machine Learning · Statistics 2017-09-07 Daniel Ting , Eric Brochu

Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…

Machine Learning · Statistics 2014-06-20 Brian McWilliams , Gabriel Krummenacher , Mario Lucic , Joachim M. Buhmann

In this paper, we study the differentiability of implicitly defined functions which we encounter in the profile likelihood estimation of parameters in semi-parametric models. Scott and Wild (Biometrika 84 (1997) 57-71; J. Statist. Plann.…

Statistics Theory · Mathematics 2016-01-08 Yuichi Hirose

This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…

Methodology · Statistics 2024-04-09 Shijie Cui , Xu Guo , Zhe Zhang

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…

Methodology · Statistics 2025-05-28 AmirEmad Ghassami , James M. Robins , Andrea Rotnitzky

For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…

Statistics Theory · Mathematics 2025-05-26 Annika Betken , Marie-Christine Düker

Predicting scalar outcomes using functional predictors is a classic problem in functional data analysis. In many applications, however, only specific locations or time-points of the functional predictors have an impact on the outcome. Such…

Statistics Theory · Mathematics 2020-07-14 Dominik Poß , Dominik Liebl , Alois Kneip , Hedwig Eisenbarth , Tor D. Wager , Lisa Feldman Barrett

In this work, we consider causal inference in various high-dimensional treatment settings, including for single multi-valued treatments and vector treatments with binary or continuous components, when the number of treatments can be…

Statistics Theory · Mathematics 2026-02-26 Patrick Kramer , Edward H. Kennedy , Isaac M. Opper

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Statistics Theory · Mathematics 2023-01-18 Wenlong Mou , Peng Ding , Martin J. Wainwright , Peter L. Bartlett

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…

Statistics Theory · Mathematics 2015-09-25 Markus Reiß , Leonie Selk

This paper proposes methods of estimation and uniform inference for a general class of causal functions, such as the conditional average treatment effects and the continuous treatment effects, under multiway clustering. The causal function…

Econometrics · Economics 2024-09-11 Nan Liu , Yanbo Liu , Yuya Sasaki

We consider a longitudinal data structure consisting of baseline covariates, time-varying treatment variables, intermediate time-dependent covariates, and a possibly time dependent outcome. Previous studies have shown that estimating the…

Statistics Theory · Mathematics 2018-10-09 Linh Tran , Maya Petersen , Joshua Schwab , Mark J van der Laan

We present a new finite-sample analysis of M-estimators of locations in $\mathbb{R}^d$ using the tool of the influence function. In particular, we show that the deviations of an M-estimator can be controlled thanks to its influence function…

Statistics Theory · Mathematics 2022-08-23 Timothée Mathieu

Causal inference from observational data is an ambitious but highly relevant task, with diverse applications ranging from natural to social sciences. Within the scope of nonparametric time series, causal inference defined through…

Methodology · Statistics 2016-12-22 Shu Li , Jan Ernest , Peter Bühlmann

This paper aims to provide a tutorial for upper level undergraduate and graduate students in statistics, biostatistics and epidemiology on deriving influence functions for non-parametric and semi-parametric models. The author will build on…

Statistics Theory · Mathematics 2019-03-12 Jonathan Levy

Influence functions approximate the effect of training samples in test-time predictions and have a wide variety of applications in machine learning interpretability and uncertainty estimation. A commonly-used (first-order) influence…

Machine Learning · Computer Science 2021-02-12 Samyadeep Basu , Philip Pope , Soheil Feizi

Statistical inference for high dimensional parameters (HDPs) can be based on their intrinsic correlation; that is, parameters that are close spatially or temporally tend to have more similar values. This is why nonlinear mixed-effects…

Methodology · Statistics 2024-01-30 Nan Zheng , Noel Cadigan