相关论文: Higher criticism for detecting sparse heterogeneou…

Clustering methods such as k-means have found widespread use in a variety of applications. This paper proposes a formal testing procedure to determine whether a null hypothesis of a single cluster, indicating homogeneity of the data, can be…

We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…

In this paper, we present a new classifier, which integrates significance testing results over different random subspaces to yield consensus p-values for quantifying the uncertainty of classification decision. The null hypothesis is that…

Testing the homogeneity between two samples of functional data is an important task. While this is feasible for intensely measured functional data, we explain why it is challenging for sparsely measured functional data and show what can be…

In the field of multiple hypothesis testing, combining p-values represents a fundamental statistical method. The Cauchy combination test (CCT) (Liu and Xie, 2020) excels among numerous methods for combining p-values with powerful and…

We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…

Factor analysis is over a century old, but it is still problematic to choose the number of factors for a given data set. The scree test is popular but subjective. The best performing objective methods are recommended on the basis of…

In high-dimensional linear models, the sparsity assumption is typically made, stating that most of the parameters are equal to zero. Under the sparsity assumption, estimation and, recently, inference have been well studied. However, in…

In this paper, we study the problem of testing whether or not a given probability measure $\mu$ on $\mathbb{R}^{d}$ can be decomposed as a mixture of two probability measures whose second order statistics are significantly different. We…

A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…

Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…

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…

Emerging applications of sensor networks for detection sometimes suggest that classical problems ought be revisited under new assumptions. This is the case of binary hypothesis testing with independent - but not necessarily identically…

Null hypothesis statistical significance testing (NHST) is the dominant approach for evaluating results from randomized controlled trials. Whereas NHST comes with long-run error rate guarantees, its main inferential tool -- the $p$-value --…

We investigate one/two-sample mean tests for high-dimensional compositional data when the number of variables is comparable with the sample size, as commonly encountered in microbiome research. Existing methods mainly focus on max-type test…

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

Significance tests are probably the most extended form of inference in empirical research, and significance is often interpreted as providing greater informational content than non-significance. In this article we show, however, that…

In many fields of research null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious…

Classification and clustering are both important topics in statistical learning. A natural question herein is whether predefined classes are really different from one another, or whether clusters are really there. Specifically, we may be…

It is frequently of interest to jointly analyze two paired sequences of multiple tests. This paper studies the problem of detecting whether there are more pairs of tests that are significant in both sequences than would be expected by…