Related papers: Pivotal Quantities with Arbitrary Small Skewness
Taylor's power law (or fluctuation scaling) states that on comparable populations, the variance of each sample is approximately proportional to a power of the mean of the population. It has been shown to hold by empirical observations in a…
In cluster randomized controlled trials (CRCT) with a finite populations, the exact design-based variance of the Horvitz-Thompson (HT) estimator for the average treatment effect (ATE) depends on the joint distribution of unobserved…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
The question of how individual patient data from cohort studies or historical clinical trials can be leveraged for designing more powerful, or smaller yet equally powerful, clinical trials becomes increasingly important in the era of…
We introduce a new multiple type I error criterion for clinical trials with multiple populations. Such trials are of interest in precision medicine where the goal is to develop treatments that are targeted to specific sub-populations…
Paired cluster-randomized experiments (pCRTs) are common across many disciplines because there is often natural clustering of individuals, and paired randomization can help balance baseline covariates to improve experimental precision.…
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…
Most cluster randomized trials (CRTs) randomize fewer than 30-40 clusters in total. When performing inference for such ``small'' CRTs, it is important to use methods that appropriately account for the small sample size. When the generalized…
We discuss CLT for the global and local linear statistics of random matrices from classical compact groups. The main part of our proofs are certain combinatorial identities much in the spirit of works by Kac and Spohn.
Recent work has proposed the use of a composite hypothesis Hoeffding test for statistical anomaly detection. Setting an appropriate threshold for the test given a desired false alarm probability involves approximating the false alarm…
This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability models (or ratio of constants) is a fundamental issue in many…
In this note, we propose a robustified analogue of the conventional Student $t$-test statistic. The proposed statistic is easy to implement and thus practically useful. We also show that it is a pivotal quantity and converges to a standard…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
Modified estimators for the contribution rates of population eigenvalues are given under an elliptically contoured distribution. These estimators decrease the bias of the classical estimator, i.e. the sample contribution rates. The…
Central limit theorems (CLTs) for high-dimensional random vectors with dimension possibly growing with the sample size have received a lot of attention in the recent times. Chernozhukov et al. (2017) proved a Berry--Esseen type result for…
Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated or otherwise generated. Typically, by selecting largest…
We consider an urn model with multiple drawing and random time-dependent addition matrix. The model is very general with respect to previous literature: the number of sampled balls at each time-step is random, the addition matrix has…
Confidence measures for the generalization error are crucial when small training samples are used to construct classifiers. A common approach is to estimate the generalization error by resampling and then assume the resampled estimator…
We seek to understand the probability an individual benefits from treatment (PIBT), an inestimable quantity that must be bounded in practice. Given the innate uncertainty in the population-level bounds on PIBT, we seek to better understand…
Autoregressive Large Language Models (LLMs) trained for next-word prediction have demonstrated remarkable proficiency at producing coherent text. But are they equally adept at forming coherent probability judgments? We use probabilistic…