Related papers: Technical Report: Higher Order Influence Functions…
We present a theory of point and interval estimation for nonlinear functionals in parametric, semi-, and non-parametric models based on higher order influence functions (Robins (2004), Section 9; Li et al. (2004), Tchetgen et al. (2006),…
Robins et al. (2008, 2017) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean $\psi$ of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous…
Methods that rely on proxies, without imposing strong parametric structure, are increasingly used to deal with unobserved variables in causal inference. One influential line of this work reconstructs latent distributions used to identify…
Higher-Order Influence Functions (HOIFs) provide a unified theory for constructing rate-optimal estimators for a large class of low-dimensional (smooth) statistical functionals/parameters (and sometimes even infinite-dimensional functions)…
We review higher order tangent spaces and influence functions and their use to construct minimax efficient estimators for parameters in high-dimensional semiparametric models.
We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…
This paper introduces a direct differentiation-based framework that unifies the derivation of influence functions across parametric, nonparametric, and semiparametric models. We show that the Riesz representer of the functional derivative…
We propose and analyze estimators for statistical functionals of one or more distributions under nonparametric assumptions. Our estimators are based on the theory of influence functions, which appear in the semiparametric statistics…
We consider the problem of estimating a dose-response curve. Continuous treatments arise often in practice, e.g. in the form of time spent on an operation, distance traveled to a location or dosage of a drug. Letting $A$ denote a continuous…
With the rapid adoption of machine learning systems in sensitive applications, there is an increasing need to make black-box models explainable. Often we want to identify an influential group of training samples in a particular test…
Robins et al. (2008) introduced a class of influence functions (IFs) which could be used to obtain doubly robust moment functions for the corresponding parameters. However, that class does not include the IF of parameters for which the…
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…
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…
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…
Influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations. For high-dimensional data, it is particularly so, as the increased dimensionality and complexity…
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…
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…
Higher-order information theory has become a rapidly growing toolkit in computational neuroscience, motivated by the idea that multivariate dependencies can reveal aspects of neural computation and communication that are invisible to…
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…
As machine learning is increasingly deployed in the real world, it is paramount that we develop the tools necessary to analyze the decision-making of the models we train and deploy to end-users. Recently, researchers have shown that…