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Wenge Guo

Publications and source records attributed to Wenge Guo.

24 records · Page 2Linked to original sources
arXiv2016

On Stepwise Control of Directional Errors under Independence and Some Dependence

In this paper, the problem of error control of stepwise multiple testing procedures is considered. For two-sided hypotheses, control of both type 1 and type 3 (or directional) errors is required, and thus mixed directional familywise error rate control and mixed directional false discovery rate control are each considered by incorporating both types of errors in the error rate. Mixed directional familywise error rate control of stepwise methods in multiple testing has proven to be a challenging problem, as demonstrated in Shaffer (1980). By an appropriate formulation of the problem, some new stepwise procedures are developed that control type 1 and directional errors under independence and various dependencies.

math.ST↗
arXiv2014

Further results on controlling the false discovery proportion

The probability of false discovery proportion (FDP) exceeding $γ\in[0,1)$, defined as $γ$-FDP, has received much attention as a measure of false discoveries in multiple testing. Although this measure has received acceptance due to its relevance under dependency, not much progress has been made yet advancing its theory under such dependency in a nonasymptotic setting, which motivates our research in this article. We provide a larger class of procedures containing the stepup analog of, and hence more powerful than, the stepdown procedure in Lehmann and Romano [Ann. Statist. 33 (2005) 1138-1154] controlling the $γ$-FDP under similar positive dependence condition assumed in that paper. We offer better alternatives of the stepdown and stepup procedures in Romano and Shaikh [IMS Lecture Notes Monogr. Ser. 49 (2006a) 33-50, Ann. Statist. 34 (2006b) 1850-1873] using pairwise joint distributions of the null $p$-values. We generalize the notion of $γ$-FDP making it appropriate in situations where one is willing to tolerate a few false rejections or, due to high dependency, some false rejections are inevitable, and provide methods that control this generalized $γ$-FDP in two different scenarios: (i) only the marginal $p$-values are available and (ii) the marginal $p$-values as well as the common pairwise joint distributions of the null $p$-values are available, and assuming both positive dependence and arbitrary dependence conditions on the $p$-values in each scenario. Our theoretical findings are being supported through numerical studies.

math.ST↗
arXiv2012

Identifying the orbital angular momentum of light based on atomic ensembles

We propose a scheme to distinguish the orbital angular momentum state of the Laguerre-Gaussian (LG) beam based on the electromagnetically induced transparency modulated by a microwave field in atomic ensembles. We show that the transverse phase variation of a probe beam with the LG mode can be mapped into the spatial intensity distribution due to the change of atomic coherence caused by the microwave. The proposal may provide a useful tool for studying higher-dimensional quantum information based on atomic ensembles.

physics.atom-ph↗
arXiv2009

On a generalized false discovery rate

The concept of $k$-FWER has received much attention lately as an appropriate error rate for multiple testing when one seeks to control at least $k$ false rejections, for some fixed $k\ge 1$. A less conservative notion, the $k$-FDR, has been introduced very recently by Sarkar [Ann. Statist. 34 (2006) 394--415], generalizing the false discovery rate of Benjamini and Hochberg [J. Roy. Statist. Soc. Ser. B 57 (1995) 289--300]. In this article, we bring newer insight to the $k$-FDR considering a mixture model involving independent $p$-values before motivating the developments of some new procedures that control it. We prove the $k$-FDR control of the proposed methods under a slightly weaker condition than in the mixture model. We provide numerical evidence of the proposed methods' superior power performance over some $k$-FWER and $k$-FDR methods. Finally, we apply our methods to a real data set.

math.ST↗
arXiv2008

On Stepwise Control of the Generalized Familywise Error Rate

A classical approach for dealing with the multiple testing problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of at least one false rejection. In many applications, one might be willing to tolerate more than one false rejection provided the number of such cases is controlled, thereby increasing the ability of the procedure to detect false null hypotheses. This suggests replacing control of the FWER by controlling the probability of $k$ or more false rejections, which is called the $k$-FWER. In this article, a unified approach is presented for deriving the $k$-FWER controlling procedures. We first generalize the well-known closure principle in the context of the FWER to the case of controlling the $k$-FWER. Then, we discuss how to derive the $k$-FWER controlling stepwise (stepdown or stepup) procedures based on marginal $p$-values using this principle. We show that, under certain conditions, generalized closed testing procedures can be reduced to stepwise procedures, and any stepwise procedure is equivalent to a generalized closed testing procedure. Finally, we generalize the well-known Hommel procedure in two directions, and show that any generalized Hommel procedure is equivalent to a generalized closed testing procedure with the same critical values.

math.ST↗