Related papers: Influence Functions for Machine Learning: Nonparam…

Evaluation of treatment effects and more general estimands is typically achieved via parametric modelling, which is unsatisfactory since model misspecification is likely. Data-adaptive model building (e.g. statistical/machine learning) is…

Many useful parameters depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a…

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…

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…

Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…

In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…

Despite the risk of misspecification they are tied to, parametric models continue to be used in statistical practice because they are accessible to all. In particular, efficient estimation procedures in parametric models are simple to…

Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of…

Parameter estimation in empirical fields is usually undertaken using parametric models, and such models readily facilitate statistical inference. Unfortunately, they are unlikely to be sufficiently flexible to be able to adequately model…

Epidemiologists increasingly use causal inference methods that rely on machine learning, as these approaches can relax unnecessary model specification assumptions. While deriving and studying asymptotic properties of such estimators is a…

Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway specific effects.…

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…

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…

Influence functions efficiently estimate the effect of removing a single training data point on a model's learned parameters. While influence estimates align well with leave-one-out retraining for linear models, recent works have shown this…

The minimum divergence estimators have proved to be useful tools in the area of robust inference. The robustness of such estimators are measured using the classical Influence functions. However, in many complex situations like testing a…

The goal of data attribution is to trace the model's predictions through the learning algorithm and back to its training data. thereby identifying the most influential training samples and understanding how the model's behavior leads to…

We consider statistical inference for a finite-dimensional parameter in a regular semiparametric model under a distributed setting with blockwise missingness, where entire blocks of variables are unavailable at certain sites and sharing…

The empirical distribution function assigns mass $1/n$ to each of the $n$ observations in a sample. As these are highly variable, estimation error may be reduced by replacing them with estimated observations that are asymptotically less…

Influence functions approximate how removing a training example changes a quantity of interest, called the target function, such as a held-out loss. To estimate the influence of a group of examples, the standard practice is to sum the…

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…