Related papers: Power in High-Dimensional Testing Problems
The random self-reinforcement mechanism, characterized by the principle of ``the rich get richer'', has demonstrated significant utility across various domains. One prominent model embodying this mechanism is the random reinforcement urn…
In shape-constrained nonparametric inference, it is often necessary to perform preliminary tests to verify whether a probability mass function (p.m.f.) satisfies qualitative constraints such as monotonicity, convexity, or in general…
Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
Data augmentation is a popular pre-processing trick to improve generalization accuracy. It is believed that by processing augmented inputs in tandem with the original ones, the model learns a more robust set of features which are shared…
Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…
In this paper, we introduce an innovative testing procedure for assessing individual hypotheses in high-dimensional linear regression models with measurement errors. This method remains robust even when either the X-model or Y-model is…
Due to the vast testing space, the increasing demand for effective and efficient testing of deep neural networks (DNNs) has led to the development of various DNN test case prioritization techniques. However, the fact that DNNs can deliver…
Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles of macrophages in atherosclerosis, is proposed. Using technic…
Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…
Genome-wide association analysis has generated much discussion about how to preserve power to detect signals despite the detrimental effect of multiple testing on power. We develop a weighted multiple testing procedure that facilitates the…
The object of study is the problem of testing for uniformity of the multinomial distribution. We consider tests based on symmetric statistics, defined as the sum of some function of cell-frequencies. Mainly, attention is focused on the…
Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the…
We consider the problem of detecting a rectangle of activation in a grid of sensors in d-dimensions with noisy measurements. This has applications to massive surveillance projects and anomaly detection in large datasets in which one detects…
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…
In this paper, we propose a parameter space augmentation approach that is based on "intentionally" introducing a pseudo-nuisance parameter into generalized linear models for the purpose of variance reduction. We first consider the parameter…
A contactless control of mean values and fluctuations of position and velocity of a nanoobject belongs among the key methods needed for ultra-precise nanotechnology and the upcoming quantum technology of macroscopic systems. An analysis of…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
The paper investigates properties of generalized Hermite-type processes that arise in non-central limit theorems for integral functionals of long-range dependent random fields. The case of increasing multidimensional domain asymptotics is…