Related papers: On the T-test
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…
This paper describes an R package implementing large sample tests and confidence intervals (based on the central limit theorem) for various parameters. The one and two sample mean and variance contexts are considered. The statistics for all…
We propose a new class of goodness-of-fit tests for the logistic distribution based on a characterisation related to the density approach in the context of Stein's method. This characterisation based test is a first of its kind for the…
The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…
Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…
Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…
We study a game theoretic model of standardized testing for college admissions. Students are of two types; High and Low. There is a college that would like to admit the High type students. Students take a potentially costly standardized…
We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…
The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of…
The G-normal distribution was introduced by Peng [2007] as the limiting distribution in the central limit theorem for sublinear expectation spaces. Equivalently, it can be interpreted as the solution to a stochastic control problem where we…
In this paper, we explore the modified Greenwood statistic, which, in contrast to the classical Greenwood statistic, is properly defined for random samples from any distribution. The classical Greenwood statistic, extensively examined in…
The likelihood ratio test (LRT) is widely used for comparing the relative fit of nested latent variable models. Following Wilks' theorem, the LRT is conducted by comparing the LRT statistic with its asymptotic distribution under the…
Generalizations to the permutation test are introduced to allow for situations in which the null model is not exchangeable. It is shown that the generalized permutation tests are exact, and a partial converse: that any test function that is…
Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability…
Statistical practice does not automatically follow methodological innovation. Regularization methods, widely advocated to reduce overfitting and stabilize inference, are readily available in modern software, but are not consistently used by…
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…
This paper considers the problem of testing many moment inequalities, where the number of moment inequalities ($p$) is possibly larger than the sample size ($n$). Chernozhukov et al. (2019) proposed asymptotic tests for this problem using…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…