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We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…
We consider the problem of constructing confidence intervals for the median of a response $Y \in \mathbb{R}$ conditional on features $X \in \mathbb{R}^d$ in a situation where we are not willing to make any assumption whatsoever on the…
This study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically…
In data analysis problems where we are not able to rely on distributional assumptions, what types of inference guarantees can still be obtained? Many popular methods, such as holdout methods, cross-validation methods, and conformal…
Covariate benchmarking is an important part of sensitivity analysis about omitted variable bias and can be used to bound the strength of the unobserved confounder using information and judgments about observed covariates. It is common to…
In prediction problems with more predictors than observations, it can sometimes be helpful to use a joint probability model, $\pi(Y,X)$, rather than a purely conditional model, $\pi(Y \mid X)$, where $Y$ is a scalar response variable and…
Growth charts are often more informative when they are customized per subject, taking into account prior measurements and possibly other covariates of the subject. We study a global semiparametric quantile regression model that has the…
We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds…
In practical applications, one often does not know the "true" structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal…
The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…
This paper explores strong and weak consistency of M-estimators for non-identically distributed data, extending prior work. Emphasis is given to scenarios where data is viewed as a triangular array, which encompasses distributional…
Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more…
In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…
We reexamine the classical linear regression model when the model is subject to two types of uncertainty: (i) some of covariates are either missing or completely inaccessible, and (ii) the variance of the measurement error is undetermined…
A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
This paper deals with the issue of ecological bias in ecological inference. We provide an explicit formulation of the conditions required for the ordinary ecological regression to produce unbiased estimates and argue that, when these…