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Heteroskedasticity poses several methodological challenges in designing valid and powerful procedures for simultaneous testing of composite null hypotheses. In particular, the conventional practice of standardizing or re-scaling…
Switchback experiments--alternating treatment and control over time--are widely used when unit-level randomization is infeasible, outcomes are aggregated, or user interference is unavoidable. In practice, experimentation must support fast…
Assume that we have a random sample from an absolutely continuous distribution (univariate, or multivariate) with a known functional form and some unknown parameters. In this paper, we have studied several parametric tests based on…
We consider inference on the first principal direction of a $p$-variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve…
In testing of hypothesis the robustness of the tests is an important concern. Generally, the maximum likelihood based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations…
Fisherian randomization inference is often dismissed as testing an uninteresting and implausible hypothesis: the sharp null of no effects whatsoever. We show that this view is overly narrow. Many randomization tests are also valid under a…
Existing sequential generalized estimating equation methodology for longitudinal and group-correlated data focuses on narrow hypotheses concerning treatment efficacy and often makes modeling assumptions that impede the desirable robustness…
Covariate adjustment is an important tool in the analysis of randomized clinical trials and observational studies. It can be used to increase efficiency and thus power, and to reduce possible bias. While most statistical tests in randomized…
In the past decades, weak convergence theory for stochastic processes has become a standard tool for analyzing the asymptotic properties of various statistics. Routinely, weak convergence is considered in the space of bounded functions…
Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…
Testing equality of two multivariate distributions is a classical problem for which many non-parametric tests have been proposed over the years. Most of the popular two-sample tests, which are asymptotically distribution-free, are based…
This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…
This work interprets and generalizes consensus-type algorithms as switching dynamics leading to symmetrization of some vector variables with respect to the actions of a finite group. We show how the symmetrization framework we develop…
In observational studies with time-to-event outcomes, the g-formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is…
When are inferences (whether Direct-Likelihood, Bayesian, or Frequentist) obtained from partial data valid? This paper answers this question by offering a new asymptotic theory about inference with missing data that is more general than…
This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in $\mathbb{R}^k$. In some places, a more general formulation in metric spaces is provided. It lays out the necessary foundation…
In any parametric inference problem, the robustness of the procedure is a real concern. A procedure which retains a high degree of efficiency under the model and simultaneously provides stable inference under data contamination is…
Random-effects models are frequently used to synthesise information from different studies in meta-analysis. While likelihood-based inference is attractive both in terms of limiting properties and of implementation, its application in…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…