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Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…
Adaptive experiments use preliminary analyses of the data to inform further course of action and are commonly used in many disciplines including medical and social sciences. Because the null hypothesis and experimental design are…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
Recently, the binary expansion testing framework was introduced to test the independence of two continuous random variables by utilizing symmetry statistics that are complete sufficient statistics for dependence. We develop a new test based…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the…
Applied researchers are increasingly interested in whether and how treatment effects vary in randomized evaluations, especially variation not explained by observed covariates. We propose a model-free approach for testing for the presence of…
A randomized trial and an analysis of observational data designed to emulate the trial sample observations separately, but have the same eligibility criteria, collect information on some shared baseline covariates, and compare the effects…
Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…
Taking a rigorous formal approach, we consider sequential decision problems involving observable variables, unobservable variables, and action variables. We can typically assume the property of extended stability, which allows…
We design sequential tests for a large class of nonparametric null hypotheses based on elicitable and identifiable functionals. Such functionals are defined in terms of scoring functions and identification functions, which are ideal…
Simultaneous statistical inference has been a cornerstone in the statistics methodology literature because of its fundamental theory and paramount applications. The mainstream multiple testing literature has traditionally considered two…
Understanding and characterizing treatment effect variation in randomized experiments has become essential for going beyond the "black box" of the average treatment effect. Nonetheless, traditional statistical approaches often ignore or…
Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials (SW-CRTs). A key consideration for analyzing a SW-CRT is accounting for the potentially complex correlation structure, which can be achieved by…
We develop a Bayesian nonparametric (BNP) approach to evaluate the causal effect of treatment in a randomized trial where a nonterminal event may be censored by a terminal event, but not vice versa (i.e., semi-competing risks). Based on the…
We propose a new method named the Conditional Randomization Rank Test (CRRT) for testing conditional independence of a response variable Y and a covariate variable X, conditional on the rest of the covariates Z. The new method generalizes…
Response-adaptive randomization (RAR) has been studied extensively in conventional, single-stage clinical trials, where it has been shown to yield ethical and statistical benefits, especially in trials with many treatment arms. However, RAR…
One central goal of design of observational studies is to embed non-experimental data into an approximate randomized controlled trial using statistical matching. Despite empirical researchers' best intention and effort to create…
The Win Ratio has gained significant traction in cardiovascular trials as a novel method for analyzing composite endpoints (Pocock and others, 2012). Compared with conventional approaches based on time to the first event, the Win Ratio…
Both cluster randomized trials and quasi-experimental designs are used to evaluate the impact of health and social policies and interventions. Stepped-wedge cluster randomized trials randomize a staggered adoption approach, while recent…