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One of the fundamental challenges found throughout the data sciences is to explain why things happen in specific ways, or through which mechanisms a certain variable $X$ exerts influences over another variable $Y$. In statistics and machine…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
Item nonresponse is frequently encountered in practice. Ignoring missing data can lose efficiency and lead to misleading inference. Fractional imputation is a frequentist approach of imputation for handling missing data. However, the…
This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…
Traditionally regression analysis answers questions about the relationships among variables based on the assumption that the observation values of variables are precise numbers. It has long been dominated by least squares techniques, mostly…
Many causal and structural effects depend on regressions. Examples include policy effects, average derivatives, regression decompositions, average treatment effects, causal mediation, and parameters of economic structural models. The…
In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
This paper addresses the problem of measurement errors in causal inference and highlights several algebraic and graphical methods for eliminating systematic bias induced by such errors. In particulars, the paper discusses the control of…
The inferential model (IM) framework provides valid prior-free probabilistic inference by focusing on predicting unobserved auxiliary variables. But, efficient IM-based inference can be challenging when the auxiliary variable is of higher…
We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions,…
Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment…
Mathematics is a limited component of solutions to real-world problems, as it expresses only what is expected to be true if all our assumptions are correct, including implicit assumptions that are omnipresent and often incorrect.…
Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality contraints on the observed distribution. This paper derives a general formula for such…
The paper discusses inference techniques for semiparametric models based on suitable versions of inference functions. The text contains two parts. In the first part, we review the optimality theory for non-parametric models based on the…
Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…
We study the semiparametric efficient estimation of a class of linear functionals in settings where a complete multivariate dataset is supplemented by additional datasets recording subsets of the variables of interest. These datasets are…
If a functional in an inverse problem can be estimated with parametric rate, then the minimax rate gives no information about the ill-posedness of the problem. To have a more precise lower bound, we study semiparametric efficiency in the…
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…