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Many experiments can be interpreted in terms of random processes operating according to some internal protocols. When experiments are costly or cannot be repeated only one or a few finite samples are available. In this paper we study data…
This study presents a new procedure for necessary tests of multivariate normality based on the uniform distribution on the Stiefel manifold. We demonstrate that the test statistic, which is formed by the product of the scaled residual…
Randomization testing is a fundamental method in statistics, enabling inferential tasks such as testing for (conditional) independence of random variables, constructing confidence intervals in semiparametric location models, and…
Adaptivity is an important feature of data analysis---typically the choice of questions asked about a dataset depends on previous interactions with the same dataset. However, generalization error is typically bounded in a non-adaptive…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
We prove that in many realistic cases, the ordinary sample mean after a group sequential trial is asymptotically normal if the maximal number of observations increases. We derive that it is often safe to use naive confidence intervals for…
Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…
Randomization tests are based on a re-randomization of existing data to gain data-dependent critical values that lead to exact hypothesis tests under special circumstances. However, it is not always possible to re-randomize data in…
For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and…
We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model…
Temporal dependence and the resulting autocovariances in time series data can introduce bias into ANOVA test statistics, thereby affecting their size and power. This manuscript accounts for temporal dependence in ANOVA and develops a test…
We consider a new group testing model wherein each item is a binary random variable defined by an a priori probability of being defective. We assume that each probability is small and that items are independent, but not necessarily…
Traditional analysis of variance (ANOVA) software allows researchers to test for the significance of main effects in the presence of interactions without exposure to the details of how the software encodes main effects and interactions to…
Fisher randomization tests for Neyman's null hypothesis of no average treatment effects are considered in a finite population setting associated with completely randomized experiments with more than two treatments. The consequences of using…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…
Assessment of multimedia quality relies heavily on subjective assessment, and is typically done by human subjects in the form of preferences or continuous ratings. Such data is crucial for analysis of different multimedia processing…
For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…
The analysis of variance (ANOVA) decomposition offers a systematic method to understand the interaction effects that contribute to a specific decision output. In this paper we introduce Neural-ANOVA, an approach to decompose neural networks…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…