Some Results on the Control of the False Discovery Rate under Dependence

Abstract.  Controlling the false discovery rate (FDR) is a powerful approach to multiple testing, with procedures developed with applications in many areas. Dependence among the test statistics is a common problem, and many attempts have been made to extend the procedures. In this paper, we show that a certain degree of dependence is allowed among the test statistics, when the number of tests is large, with no need for any correction. We then suggest a way to conservatively estimate the proportion of false nulls, both under dependence and independence, and discuss the advantages of using such estimators when controlling the FDR.     

Semiparametric smoothing of sparse contingency tables

In the paper simple resampling technique based on semiparametric smoothing is introduced. Although the method is very flexible and in principle can be applied to any sparse data and ill-posed statistical problem, its efficient or even reasonable implementation requires special investigation. In the paper a problem of fitting local dependence structure of finite-state random sequences is addressed. This problem is relevant, for example, in genetics, bioinformatics, computer linguistics, etc., and usually leads to analysis of sparse contingency tables of dependent categorical data. Thus, the classical assumptions of log-linear model, a standard technique for analysis of contingency tables, do not hold. A framework convenient for implementation of semiparametric smoothing and resampling is proposed. It is based on a special representation form of data under consideration and generalized logit model. A computer experiment is carried out to gain better insight on practical performance of the procedure.     

ML, PL, QL in Markov Chain Models

Abstract.  In many spatial and spatial-temporal models, and more generally in models with complex dependencies, it may be too difficult to carry out full maximum-likelihood (ML) analysis. Remedies include the use of pseudo-likelihood (PL) and quasi-likelihood (QL) (also called the composite likelihood). The present paper studies the ML, PL and QL methods for general Markov chain models, partly motivated by the desire to understand the precise behaviour of the PL and QL methods in settings where this can be analysed. We present limiting normality results and compare performances in different settings. For Markov chain models, the PL and QL methods can be seen as maximum penalized likelihood methods. We find that QL is typically preferable to PL, and that it loses very little to ML, while sometimes earning in model robustness. It has also appeal and potential as a modelling tool. Our methods are illustrated for consonant-vowel transitions in poetry and for analysis of DNA sequence evolution-type models.     

Exploring the variability of DNA molecules via principal geodesic analysis on the shape space

Most of the linear statistics deal with data lying in a Euclidean space. However, there are many examples, such as DNA molecule topological structures, in which the initial or the transformed data lie in a non-Euclidean space. To get a measure of variability in these situations, the principal component analysis (PCA) is usually performed on a Euclidean tangent space as it cannot be directly implemented on a non-Euclidean space. Instead, principal geodesic analysis (PGA) is a new tool that provides a measure of variability for nonlinear statistics. In this paper, the performance of this new tool is compared with that of the PCA using a real data set representing a DNA molecular structure. It is shown that due to the nonlinearity of space, the PGA explains more variability of the data than the PCA.     

幼女“产婴证奸”问题探析

近来,幼女＂产婴证奸＂的事件屡屡见诸报端。这一方面凸显了我国救助机制的缺失,实现正义的代价过于高昂;另一方面还引发了一些现实问题和法律难题。针对这种状况,建议完善相关立法,构建相应的社会救助机制,加强对这一群体的普法及性教育,培养其自我保护意识,避免＂产婴证奸＂现象的再次发生。     

Characterizing the reconstruction and enumerating the patterns of DNA sequences with repeats

A repeat in a DNA sequence is a substring that appears more than once. In DNA sequencing, the occurrence of repeats may hinder the unique reconstruction. In addition, the number of possible reconstructions depends on the pattern of repeats in a DNA sequence. Arratia et al. studied the patterns of DNA sequences with twofold repeats that result in k-way reconstructions. In this paper, multiple-fold repeats, including twofold repeats, are considered. For each pattern of DNA repeats, the possible reconstructions of the DNA sequence are enumerated by its reduced digraph. Then the reconstructions of DNA sequences with repeats are characterized using the pattern graphs. Finally, for DNA sequences with n repeats, the patterns of DNA repeats resulting in k-way reconstruction are enumerated. Dedicated to Professor Frank K. Hwang on the occasion of his 65th birthday.