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Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…
We present an optimized rerandomization design procedure for a non-sequential treatment-control experiment. Randomized experiments are the gold standard for finding causal effects in nature. But sometimes random assignments result in…
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic,…
The Randomized Controlled Trial (RCT) or A/B testing is considered the gold standard method for estimating causal effects. Fisher famously advocated randomly allocating experiment units into treatment and control groups to preclude…
Causal analyses for observational studies are often complicated by covariate imbalances among treatment groups, and matching methodologies alleviate this complication by finding subsets of treatment groups that exhibit covariate balance. It…
Covariate shift, a widely used assumption in tackling {\it distributional shift} (when training and test distributions differ), focuses on scenarios where the distribution of the labels conditioned on the feature vector is the same, but the…
A practical limitation of cluster randomized controlled trials (cRCTs) is that the number of available clusters may be small, resulting in an increased risk of baseline imbalance under simple randomization. Constrained randomization…
Matching is a widely used causal inference design that aims to approximate a randomized experiment using observational data by forming matched sets of treated and control units based on similarities in their covariates. Ideally, treated…
We propose novel estimators for categorical and continuous treatments by using an optimal covariate balancing strategy for inverse probability weighting. The resulting estimators are shown to be consistent and asymptotically normal for…
We propose a nonparametric procedure to test for changes in correlation matrices at an unknown point in time. The new test requires only mild assumptions on the serial dependence structure and has considerable power in finite samples. We…
The conditional randomization test (CRT) was recently proposed to test whether two random variables X and Y are conditionally independent given random variables Z. The CRT assumes that the conditional distribution of X given Z is known…
We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection…
We present a general approach to constructing permutation tests that are both exact for the null hypothesis of equality of distributions and asymptotically correct for testing equality of parameters of distributions while allowing the…
The idea of covariate balance is at the core of causal inference. Inverse propensity weights play a central role because they are the unique set of weights that balance the covariate distributions of different treatment groups. We discuss…
Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…
The first step towards investigating the effectiveness of a treatment via a randomized trial is to split the population into control and treatment groups then compare the average response of the treatment group receiving the treatment to…
Conditional independence testing (CIT) is a common task in machine learning, e.g., for variable selection, and a main component of constraint-based causal discovery. While most current CIT approaches assume that all variables are numerical…
Causality is widely used in fairness analysis to prevent discrimination on sensitive attributes, such as genders in career recruitment and races in crime prediction. However, the current data-based Potential Outcomes Framework (POF) often…
Randomized controlled trials (RCTs) are the gold standard for estimating heterogeneous treatment effects, yet they are often underpowered for detecting effect heterogeneity. Large observational studies (OS) can supplement RCTs for…
Instrumental variable (IV) analyses are becoming common in health services research and epidemiology. Most IV analyses use naturally occurring instruments, such as distance to a hospital. In these analyses, investigators must assume the…