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A/B testing is an effective way to assess the potential impacts of two treatments. For A/B tests conducted by IT companies, the test users of A/B testing are often connected and form a social network. The responses of A/B testing can be…
This paper investigates the central limit theorem for linear spectral statistics of high dimensional sample covariance matrices of the form $\mathbf{B}_n=n^{-1}\sum_{j=1}^{n}\mathbf{Q}\mathbf{x}_j\mathbf{x}_j^{*}\mathbf{Q}^{*}$ where…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
A/B testing refers to the statistical procedure of conducting an experiment to compare two treatments, A and B, applied to different testing subjects. It is widely used by technology companies such as Facebook, LinkedIn, and Netflix, to…
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…
We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…
Online controlled experiments (also known as A/B Testing) have been viewed as a golden standard for large data-driven companies since the last few decades. The most common A/B testing framework adopted by many companies use "average…
Experimentation is widely utilized for causal inference and data-driven decision-making across disciplines. In an A/B experiment, for example, an online business randomizes two different treatments (e.g., website designs) to their customers…
A/B testing is one of the most successful applications of statistical theory in modern Internet age. One problem of Null Hypothesis Statistical Testing (NHST), the backbone of A/B testing methodology, is that experimenters are not allowed…
This paper examines the use of Monte Carlo simulations to understand statistical concepts in A/B testing and Randomized Controlled Trials (RCTs). We discuss the applicability of simulations in understanding false positive rates and estimate…
Design of experiments and estimation of treatment effects in large-scale networks, in the presence of strong interference, is a challenging and important problem. Most existing methods' performance deteriorates as the density of the network…
Testing for normality is a widely used procedure in statistics and data analysis, often applied prior to employing methods that rely on the assumption of normally distributed data. While several existing tests target distributional…
A/B testing, or controlled experiments, is the gold standard approach to causally compare the performance of algorithms on online platforms. However, conventional Bernoulli randomization in A/B testing faces many challenges such as…
There is a growing literature on design-based methods to estimate average treatment effects for randomized controlled trials (RCTs) using the underpinnings of experiments. In this article, we build on these methods to consider design-based…
Generalized linear mixed models (GLMM) are commonly used to analyze clustered data, but when the number of clusters is small to moderate, standard statistical tests may produce elevated type I error rates. Small-sample corrections have been…
The batch means estimator of the MCMC variance is a simple and effective measure of accuracy for MCMC based ergodic averages. Under various regularity conditions, the estimator has been shown to be consistent for the true variance. However,…
In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial…
Many scientific questions rely on determining whether two sequences of event times are associated. This article introduces a likelihood ratio test which can be parameterised in several ways to detect different forms of dependence. A common…
Randomized experiments play a major role in data-driven decision making across many different fields and disciplines. In medicine, for example, randomized controlled trials (RCTs) are the backbone of clinical trial methodology for testing…
In many industry settings, online controlled experimentation (A/B test) has been broadly adopted as the gold standard to measure product or feature impacts. Most research has primarily focused on user engagement type metrics, specifically…