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Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…
We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample…
Contextual sensing and delivery of digital interventions to improve health outcomes have gained significant traction in behavioral and psychiatric studies. Micro-randomized trials (MRTs) are a common experimental design for obtaining…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
Data augmentation is popular in the training of large neural networks; currently, however, there is no clear theoretical comparison between different algorithmic choices on how to use augmented data. In this paper, we take a step in this…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the…
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
Demand response is designed to motivate electricity customers to modify their loads at critical time periods. The accurate estimation of impact of demand response signals to customers' consumption is central to any successful program. In…
This paper studies the use of a machine learning-based estimator as a control variate for mitigating the variance of Monte Carlo sampling. Specifically, we seek to uncover the key factors that influence the efficiency of control variates in…
Penalties that induce smoothness are common in nonparametric regression. In many settings, the amount of smoothness in the data generating function will not be known. Simon and Shojaie (2021) derived convergence rates for nonparametric…
Randomized controlled trials (RCTs) often include subgroup analyses to assess whether treatment effects vary across pre-specified patient populations. However, these analyses frequently suffer from small sample sizes which limit the power…
This paper develops an empirical balancing approach for the estimation of treatment effects under two-sided noncompliance using a binary conditionally independent instrumental variable. The method weighs both treatment and outcome…
Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building…
We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator…
There has been a split in the statistics community about the need for taking covariates into account in the design phase of a clinical trial. There are many advocates of using stratification and covariate-adaptive randomization to promote…
It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This…
This work examines the optimal covariance steering problem for systems subject to unknown parameters that enter multiplicatively with the state and control, in addition to additive disturbances. In contrast to existing works, the unknown…
We consider linear regression model estimation where the covariate of interest is randomly censored. Under a non-informative censoring mechanism, one may obtain valid estimates by deleting censored observations. However, this comes at a…
We study targeted maximum likelihood estimation (TMLE) of the average treatment effect in a semiparametric regression model whose mean function is indexed by a finite-dimensional parameter, while the additive error distribution is left…