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We propose a semiparametric framework for causal inference with right-censored survival outcomes and many weak invalid instruments, motivated by Mendelian randomization in biobank studies where classical methods may fail. We adopt an…
Consider $M$-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found…
Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…
Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian…
The classical parametric and semiparametric Bernstein -- von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain…
We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional…
Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…
This study proposes a framework for estimating demand in differentiated product markets with high dimensional product characteristics, building upon the seminal Berry, Levinsohn, and Pakes (1995) model, using market level data. We allow for…
This paper develops a two-stage method for inference on partially identified parameters in moment inequality models with separable nuisance parameters. In the first stage, the nuisance parameters are estimated separately, and in the second…
We propose double/debiased machine learning approaches to infer (at the parametric rate) the parametric component of a logistic partially linear model with the binary response following a conditional logistic model of a low dimensional…
The simultaneous estimation of multiple unknown parameters lies at heart of a broad class of important problems across science and technology. Currently, the state-of-the-art performance in the such problems is achieved by nonparametric…
We provide non-asymptotic excess risk guarantees for statistical learning in a setting where the population risk with respect to which we evaluate the target parameter depends on an unknown nuisance parameter that must be estimated from…
There is a wide range of applications where the local extrema of a function are the key quantity of interest. However, there is surprisingly little work on methods to infer local extrema with uncertainty quantification in the presence of…
Instrumental variable (IV) methods are widely used to infer treatment effects in the presence of unmeasured confounding. In this paper, we study nonparametric inference with an IV under a separable binary treatment choice model, which…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
We study the Gaussian sequence compound decision problem and analyze a Bayesian nonparametric estimator from an empirical Bayes, regret-based perspective. Motivated by sharp results for the classical nonparametric maximum likelihood…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
Ordinary differential equations (ODEs) are used to model dynamic systems appearing in engineering, physics, biomedical sciences and many other fields. These equations contain unknown parameters, say $\bm\theta$ of physical significance…
We study inference on a low-dimensional functional $\beta$ in the presence of infinite-dimensional nuisance parameters. Classical inferential methods are typically based on Wald intervals, whose large-sample validity rests on asymptotic…
Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is complicated because the effect of estimating the…