Limit theorems for functions of marginal quantiles

Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a strong law of large numbers. A result similar to Bahadur's representation of quantiles is established for the mean of a function of the marginal quantiles. In particular, it is shown that $$\sqrt{n}\Biggl(\frac{1}{n}\sum_{i=1}^n\phi\bigl(X_{n:i}^{(1)},...,X_{n:i}^{(d)}\bigr)-\bar{\gamma}\Biggr)=\frac{1}{\sqrt{n}}\sum_{i=1}^nZ_{n,i}+\mathrm{o}_P(1)$$ as $n\rightarrow\infty$, where $\bar{\gamma}$ is a constant and $Z_{n,i}$ are i.i.d. random variables for each $n$. This leads to the central limit theorem. Weak convergence to a Gaussian process using equicontinuity of functions is indicated. The results are established under very general conditions. These conditions are shown to be satisfied in many commonly occurring situations.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ287 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

AT excursion: a new approach to predict replication origins in viral genomes by locating AT-rich regions

<p>Abstract</p> <p>Background</p> <p>Replication origins are considered important sites for understanding the molecular mechanisms involved in DNA replication. Many computational methods have been developed for predicting their locations in archaeal, bacterial and eukaryotic genomes. However, a prediction method designed for a particular kind of genomes might not work well for another. In this paper, we propose the AT excursion method, which is a score-based approach, to quantify local AT abundance in genomic sequences and use the identified high scoring segments for predicting replication origins. This method has the advantages of requiring no preset window size and having rigorous criteria to evaluate statistical significance of high scoring segments.</p> <p>Results</p> <p>We have evaluated the AT excursion method by checking its predictions against known replication origins in herpesviruses and comparing its performance with an existing base weighted score method (BWS₁). Out of 43 known origins, 39 are predicted by either one or the other method and 26 origins are predicted by both. The excursion method identifies six origins not predicted by BWS₁, showing that the AT excursion method is a valuable complement to BWS₁. We have also applied the AT excursion method to two other families of double stranded DNA viruses, the poxviruses and iridoviruses, of which very few replication origins are documented in the public domain. The prediction results are made available as supplementary materials at <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>. Preliminary investigation shows that the proposed method works well on some larger genomes too.</p> <p>Conclusion</p> <p>The AT excursion method will be a useful computational tool for identifying replication origins in a variety of genomic sequences.</p

A post-processing method for optimizing synthesis strategy for oligonucleotide microarrays

The broad applicability of gene expression profiling to genomic analyses has generated huge demand for mass production of microarrays and hence for improving the cost effectiveness of microarray fabrication. We developed a post-processing method for deriving a good synthesis strategy. In this paper, we assessed all the known efficient methods and our post-processing method for reducing the number of synthesis cycles for manufacturing a DNA-chip of a given set of oligos. Our experimental results on both simulated and 52 real datasets show that no single method consistently gives the best synthesis strategy, and post-processing an existing strategy is necessary as it often reduces the number of synthesis cycles further

ConReg-R: Extrapolative recalibration of the empirical distribution of p-values to improve false discovery rate estimates

<p>Abstract</p> <p>Background</p> <p>False discovery rate (FDR) control is commonly accepted as the most appropriate error control in multiple hypothesis testing problems. The accuracy of FDR estimation depends on the accuracy of the estimation of p-values from each test and validity of the underlying assumptions of the distribution. However, in many practical testing problems such as in genomics, the p-values could be under-estimated or over-estimated for many known or unknown reasons. Consequently, FDR estimation would then be influenced and lose its veracity.</p> <p>Results</p> <p>We propose a new extrapolative method called <it>Constrained Regression Recalibration </it>(ConReg-R) to recalibrate the empirical p-values by modeling their distribution to improve the FDR estimates. Our ConReg-R method is based on the observation that accurately estimated p-values from true null hypotheses follow uniform distribution and the observed distribution of p-values is indeed a mixture of distributions of p-values from true null hypotheses and true alternative hypotheses. Hence, ConReg-R recalibrates the observed p-values so that they exhibit the properties of an ideal empirical p-value distribution. The proportion of true null hypotheses (<it>π</it>₀) and FDR are estimated after the recalibration.</p> <p>Conclusions</p> <p>ConReg-R provides an efficient way to improve the FDR estimates. It only requires the p-values from the tests and avoids permutation of the original test data. We demonstrate that the proposed method significantly improves FDR estimation on several gene expression datasets obtained from microarray and RNA-seq experiments.</p> <p>Reviewers</p> <p>The manuscript was reviewed by Prof. Vladimir Kuznetsov, Prof. Philippe Broet, and Prof. Hongfang Liu (nominated by Prof. Yuriy Gusev).</p

On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees

Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolutionary relationships among taxonomic units ranging from viruses to species. We study two subtree counting statistics, the number of cherries and the number of pitchforks, for random phylogenetic trees generated by two widely used null tree models: the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. By developing limit theorems for a version of extended Pólya urn models in which negative entries are permitted for their replacement matrices, we deduce the strong laws of large numbers and the central limit theorems for the joint distributions of these two counting statistics for the PDA and the YHK models. Our results indicate that the limiting behaviour of these two statistics, when appropriately scaled using the number of leaves in the underlying trees, is independent of the initial tree used in the tree generating process

On cherry and pitchfork distributions of random rooted and unrooted phylogenetic trees

Tree shape statistics are important for investigating evolutionary mechanisms mediating phylogenetic trees. As a step towards bridging shape statistics between rooted and unrooted trees, we present a comparison study on two subtree statistics known as numbers of cherries and pitchforks for the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. Based on recursive formulas on the joint distribution of the number of cherries and that of pitchforks, it is shown that cherry distributions are log-concave for both rooted and unrooted trees under these two models. Furthermore, the mean number of cherries and that of pitchforks for unrooted trees converge respectively to those for rooted trees under the YHK model while there exists a limiting gap of 1/4 for the PDA model. Finally, the total variation distances between the cherry distributions of rooted and those of unrooted trees converge for both models. Our results indicate that caution is required for conducting statistical analysis for tree shapes involving both rooted and unrooted trees

Service Quality of Online Shopping Platforms: A Case-Based Empirical and Analytical Study

Customer service is crucially important for online shopping platforms (OSPs) such as eBay and Taobao. Based on the well-established service quality instruments and the scenario of the specific case on Taobao, this paper focuses on exploring the service quality of an OSP with an aim of revealing customer perceptions of the service quality associated with the provided functions and investigating their impacts on customer loyalty. By an empirical study, this paper finds that the “fulfillment and responsiveness” function is significantly related to the customer loyalty. Further analytical study is conducted to reveal that the optimal service level on the “fulfillment and responsiveness” function for the risk averse OSP uniquely exists. Moreover, the analytical results prove that (i) if the customer loyalty is more positively correlated to the service level, it will lead to a larger optimal service level, and (ii) the optimal service level is independent of the profit target, the source of uncertainty, and the risk preference of the OSP

On joint subtree distributions under two evolutionary models

In population and evolutionary biology, hypotheses about micro-evolutionary and macroevolutionary processes are commonly tested by comparing the shape indices of empirical evolutionary trees with those predicted by neutral models. A key ingredient in this approach is the ability to compute and quantify distributions of various tree shape indices under random models of interest. As a step to meet this challenge, in this paper we investigate the joint distribution of cherries and pitchforks (that is, subtrees with two and three leaves) under two widely used null models: the Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model. Based on two novel recursive formulae, we propose a dynamic approach to numerically compute the exact joint distribution (and hence the marginal distributions) for trees of any size. We also obtained insights into the statistical properties of trees generated under these two models, including a constant correlation between the cherry and the pitchfork distributions under the YHK model, and the log-concavity and unimodality of the cherry distributions under both models. In addition, we show that there exists a unique change point for the cherry distributions between these two models

A novel Hsp90 inhibitor AT13387 induces senescence in EBV-positive nasopharyngeal carcinoma cells and suppresses tumor formation

Background: Nasopharyngeal carcinoma (NPC) is an epithelial malignancy strongly associated with Epstein-Barr virus (EBV). AT13387 is a novel heat shock protein 90 (Hsp90) inhibitor, which inhibits the chaperone function of Hsp90 and reduces expression of Hsp90-dependent client oncoproteins. This study aimed to evaluate both the in vitro and in vivo antitumor effects of AT13387 in the EBV-positive NPC cell line C666-1.Results: Our results showed that AT13387 inhibited C666-1 cell growth and induced cellular senescence with the downregulation of multiple Hsp90 client oncoproteins EGFR, AKT, CDK4, and restored the protein expression of negative cell cycle regulator p27. We also studied the ability of AT13387 to restore p27 expression by downregulation of AKT and the p27 ubiquitin mediator, Skp2, using AKT inhibitor and Skp2 siRNA. In the functional study, AT13387 inhibited cell migration with downregulation of a cell migration regulator, HDAC6, and increased the acetylation and stabilization of α-tubulin. We also examined the effect of AT13387 on putative cancer stem cells (CSC) by 3-D tumor sphere formation assay. AT13387 effectively reduced both the number and size of C666-1 tumor spheres with decreased expression of NPC CSC-like markers CD44 and SOX2. In the in vivo study, AT13387 significantly suppressed tumor formation in C666-1 NPC xenografts.Conclusion: AT13387 suppressed cell growth, cell migration, tumor sphere formation and induced cellular senescence on EBV-positive NPC cell line C666-1. Also, the antitumor effect of AT13387 was demonstrated in an in vivo model. This study provided experimental evidence for the preclinical value of using AT13387 as an effective antitumor agent in treatment of NPC. © 2013 Chan et al.; licensee BioMed Central Ltd.published_or_final_versio

Sharp bounds and normalization of Wiener-type indices

10.1371/journal.pone.0078448PLoS ONE811-POLN