Modular-transform based clustering

Spectral clustering uses eigenvectors of the Laplacian of the similarity matrix. It is convenient to solve binary clustering problems. When applied to multi-way clustering, either the binary spectral clustering is recursively applied or an embedding to spectral space is done and some other methods, such as K-means clustering, are used to cluster the points. Here we propose and study a K-way clustering algorithm – spectral modular transformation, based on the fact that the graph Laplacian has an equivalent representation, which has a diagonal modular structure. The method first transforms the original similarity matrix into a new one, which is nearly disconnected and reveals a cluster structure clearly, then we apply linearized cluster assignment algorithm to split the clusters. In this way, we can find some samples for each cluster recursively using the divide and conquer method. To get the overall clustering results, we apply the cluster assignment obtained in the previous step as the initialization of multiplicative update method for spectral clustering. Examples show that our method outperforms spectral clustering using other initializations.     

A note on statistical method for genotype calling of high-throughput single-nucleotide polymorphism arrays

We study the genotype calling algorithms for the high-throughput single-nucleotide polymorphism (SNP) arrays. Building upon the novel SNP-robust multi-chip average preprocessing approach and the state-of-the-art corrected robust linear model with Mahalanobis distance (CRLMM) approach for genotype calling, we propose a simple modification to better model and combine the information across multiple SNPs with empirical Bayes modeling, which could often significantly improve the genotype calling of CRLMM. Through applications to the HapMap Trio data set and a non-HapMap test set of high quality SNP chips, we illustrate the competitive performance of the proposed method.     

机构投资者异质性的上市公司股利政策研究

 本文从现金股利政策的角度来研究机构投资者的投资行为和参与上市公司治理的情况。首先回顾了该方面的相关文献,以信号理论为基础,分析机构投资者与现金股利政策可能存在的关系;接着对机构投资者的基本特征以及我国机构投资者和上市公司现金股利政策的概况及特点进行了总结;最后本文以 2007至2010 年的机构投资者持股数据与上市公司现金股利政策数据进行统计分析、回归分析,实证检验了机构投资者异质性与上市公司股利政策之间的关系。     

Reducing bias of the maximum-likelihood estimation for the truncated Pareto distribution

The Pareto distribution is an important distribution in statistics, which has been widely used in finance, physics, hydrology, geology, astronomy, and so on. Even though the parameter estimation for the Pareto distribution has been well established in the literature, the estimation problem for the truncated Pareto distribution becomes complex. This article investigates the bias and mean-squared error of the maximum-likelihood estimation for the truncated Pareto distribution, and some useful results are obtained.     

Model averaging for M-estimation

M-estimation is a widely used technique for robust statistical inference. In this paper, we study model selection and model averaging for M-estimation to simultaneously improve the coverage probability of confidence intervals of the parameters of interest and reduce the impact of heavy-tailed errors or outliers in the response. Under general conditions, we develop robust versions of the focused information criterion and a frequentist model average estimator for M-estimation, and we examine their theoretical properties. In addition, we carry out extensive simulation studies as well as two real examples to assess the performance of our new procedure, and find that the proposed method produces satisfactory results.     

A Multivariate Synthetic Control Chart for Monitoring the Process Mean Vector of Skewed Populations Using Weighted Standard Deviations

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method. The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart. The standard multivariate synthetic chart consists of the Hotelling's T ² chart and the conforming run length chart. The weighted standard deviation method adjusts the variance–covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric. In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T ² chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses.     

Operating Characteristics for Group Sequential Trials Monitored Under Fractional Brownian Motion

Brownian motion has been used to derive stopping boundaries for group sequential trials, however, when we observe dependent increment in the data, fractional Brownian motion is an alternative to be considered to model such data. In this article we compared expected sample sizes and stopping times for different stopping boundaries based on the power family alpha spending function under various values of Hurst coefficient. Results showed that the expected sample sizes and stopping times will decrease and power increases when the Hurst coefficient increases. With same Hurst coefficient, the closer the boundaries are to that of O'Brien-Fleming, the higher the expected sample sizes and stopping times are; however, power has a decreasing trend for values start from H = 0.6 (early analysis), 0.7 (equal space), 0.8 (late analysis). We also illustrate study design changes using results from the BHAT study.     

Out-of-Bag Estimation of the Optimal Hyperparameter in SubBag Ensemble Method

SubBag is a technique by combining bagging and random subspace methods to generate ensemble classifiers with good generalization capability. In practice, a hyperparameter K of SubBag—the number of randomly selected features to create each base classifier—should be specified beforehand. In this article, we propose to employ the out-of-bag instances to determine the optimal value of K in SubBag. The experiments conducted with some UCI real-world data sets show that the proposed method can make SubBag achieve the optimal performance in nearly all the considered cases. Meanwhile, it occupied less computational sources than cross validation procedure.     

A Note on the Likelihood Ratio Test for Equality of k Normal Populations

The authors derive the analytic expressions for the mean and variance of the log-likelihood ratio for testing equality of k (k ≥ 2) normal populations, and suggest a chi-square approximation and a gamma approximation to the exact null distribution. Numerical comparisons show that the two approximations and the original beta approximation of Neyman and Pearson (1931 Neyman , J. , Pearson , E. S. ( 1931 ). On the problem of k samples . In: Neyman , J. , Pearson , E. S. , eds. Joint Statistical Papers . Cambridge : Cambridge University Press , pp. 116 – 131 . [Google Scholar]) are all accurate, and the gamma approximation is the most accurate.