Journal of Data Science

Abstract: We analyze the cross-correlation between logarithmic returns of 1108 stocks listed on the Shanghai and Shenzhen Stock Exchange of China in the period 2005 to 2010. The results suggest that the estimated distribution of correlation coefficients is right shifted in the tumble time of Chinese stock market. Due to the large share of maximum eigenvalue, the principal correlation component in Chinese stock market is dominant and other components only have trivial effects on the market condition. The same-signed corresponding vector elements enable us to propose the maximum eigenvalue series as an indicator for collective behavior in the equity market. We provide the evidence that the largest eigenvalue series can be used as an effective indicative parameter to describe the collective behavior of stock returns, which is found to be positively correlated to market volatility. By using time-varying windows, we find the positive correlation diminishes when the market volatility reaches both highest and lowest level. By defining a stability rate, we display that the collective behavior of stocks tends to be more homogeneous in the context of crisis than the regular time. This study has implications for the arising discussions on correlation risk.

Abstract: Family background factor can be a very important part of a person’s life. One of the main interests of this paper is to investigate whether the family background factors alter performance on mathematical achievement of the stronger students the same way that weaker students are affected. Using large sample of 2000, 2001 and 2002 mathematics participation in Alberta, Canada, such questions have been investigated by means of quantile regression approach. The findings suggest that there may be differential family-background-factor effects at different points in the conditional distribution of mathematical achievements.

Abstract: Considering the importance of science and mathematics achieve ments of young students, one of the most well known observed phenomenon is that the performance of U.S. students in mathematics and sciences is undesirable. In order to deal with the problem of declining mathematics and science scores of American high school students, many strategies have been implemented for several decades. In this paper, we give an in-depth longitudinal study of American youth using a double-kernel approach of non parametric quantile regression. Two of the advantages of this approach are: (1) it guarantees that a Nadaraya-Watson estimator of the conditional func tion is a distribution function while, in some cases, this kind of estimator being neither monotone nor taking values only between 0 and 1; (2) it guar antees that quantile curves which are based on Nadaraya-Watson estimator not absurdly cross each other. Previous work has focused only on mean re gression and parametric quantile regression. We obtained many interesting results in this study.

As a robust data analysis technique, quantile regression has attracted extensive interest. In this study, the weighted quantile regression (WQR) technique is developed based on sparsity function. We first consider the linear regression model and show that the relative efficiency of WQR compared with least squares (LS) and composite quantile regression (CQR) is greater than 70% regardless of the error distributions. To make the pro- posed method practically more useful, we consider two nontrivial extensions. The first concerns with a nonparametric model. Local WQR estimate is introduced to explore the nonlinear data structure and shown to be much more efficient compared to other estimates under various non-normal error distributions. The second extension concerns with a multivariate problem where variable selection is needed along with regulation. We couple the WQR with penalization and show that under mild conditions, the penalized WQR en- joys the oracle property. The WQR has an intuitive formulation and can be easily implemented. Simulation is conducted to examine its finite sample performance and compare against alternatives. Analysis of mammal dataset is also conducted. Numerical studies are consistent with the theoretical findings and indicate the usefulness of WQR