Local and global rank tests for multivariate varying-coefficient models

In a multivariate varying-coefficient model, the response vectors Y are regressed on known functions u(X) of some explanatory variables X and the coefficients in an unknown regression matrix q(Z) depend on another set of explanatory variables Z. We provide statistical tests, called local and global rank tests, which allow to estimate the rank of an unknown regression coefficient matrix q(Z) locally at a fixed level of the variable Z or globally as the maximum rank over all levels of Z, respectively. In the case of local rank tests, we do so by applying already available rank tests to a kernel-based estimator of the coefficient matrix q(z). Global rank tests are obtained by integrating test statistics used in estimation of local rank tests. We present a simulation study where, focusing on global ranks, we examine small sample properties of the considered statistical tests. We also apply our results to estimate the so-called local and global ranks in a demand system where budget shares are regressed on known functions of total expenditures and the coefficients in a regression matrix depend on prices faced by a consumer.varying-coefficient model, kernel smoothing, matrix rank estimation, demand systems, local and global ranks

A Survey on Studying the Social Networks of Students

Do studies show that physical and online students' social networks support education? Analyzing interactions between students in schools and universities can provide a wealth of information. Studies on students' social networks can help us understand their behavioral dynamics, the correlation between their friendships and academic performance, community and group formation, information diffusion, and so on. Educational goals and holistic development of students with various academic abilities and backgrounds can be achieved by incorporating the findings attained by the studies in terms of knowledge propagation in classroom and spread of delinquent behaviors. Moreover, we use Social Network Analysis (SNA) to identify isolated students, ascertain the group study culture, analyze the spreading of various habits like smoking, drinking, and so on. In this paper, we present a review of the research showing how analysis of students' social networks can help us identify how improved educational methods can be used to make learning more inclusive at both school and university levels and achieve holistic development of students through expansion of their social networks, as well as control the spread of delinquent behaviors.Comment: Huso 201

An Experimental Study of Distributed Quantile Estimation

Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis. However, quite often, computing quantiles directly is inappropriate due to the memory limitations. Further, in many settings such as data streaming and sensor network model, even the data size is unpredictable. Although the quantiles computation has been widely studied, it was mostly in the sequential setting. In this paper, we study several quantile computation algorithms in the distributed setting and compare them in terms of space usage, running time, and accuracy. Moreover, we provide detailed experimental comparisons between several popular algorithms. Our work focuses on the approximate quantile algorithms which provide error bounds. Approximate quantiles have received more attentions than exact ones since they are often faster, can be more easily adapted to the distributed setting while giving sufficiently good statistical information on the data sets.Comment: M.S. Thesi

Regional Distribution, Non-invasive Detection, and Genetic Diversity of the Black-spotted Newt (Notophthalmus meridionalis)

The Black-spotted Newt (Notophthalmus meridionalis ) is one of three a salamander species native to Gulf Coast prairies of Texas and Mexico, with respective state and federal protections. This species has been neglected by the scientific community despite concerns of dramatic population declines and a globally endangered status, with the most recent work being conducted in the early 1990’s going unpublished. This study presents the most recent examination of the species providing probabilistic distribution maps, descriptions of three novel populations, assessments of surveying techniques, and the first known examination of intrapopulation genetics including the first documented genetic examination of the southern subspecies. An updated status review is provided in response to the results of this study and an expansive literature review