Covariance-regularized regression and classification for high dimensional problems

Summary.  We propose covariance-regularized regression, a family of methods for prediction in high dimensional settings that uses a shrunken estimate of the inverse covariance matrix of the features to achieve superior prediction. An estimate of the inverse covariance matrix is obtained by maximizing the log-likelihood of the data, under a multivariate normal model, subject to a penalty; it is then used to estimate coefficients for the regression of the response onto the features. We show that ridge regression, the lasso and the elastic net are special cases of covariance-regularized regression, and we demonstrate that certain previously unexplored forms of covariance-regularized regression can outperform existing methods in a range of situations. The covariance-regularized regression framework is extended to generalized linear models and linear discriminant analysis, and is used to analyse gene expression data sets with multiple class and survival outcomes.     

On pseudo-values for regression analysis in competing risks models

For regression on state and transition probabilities in multi-state models Andersen et al. (Biometrika 90:15–27, 2003) propose a technique based on jackknife pseudo-values. In this article we analyze the pseudo-values suggested for competing risks models and prove some conjectures regarding their asymptotics (Klein and Andersen, Biometrics 61:223–229, 2005). The key is a second order von Mises expansion of the Aalen-Johansen estimator which yields an appropriate representation of the pseudo-values. The method is illustrated with data from a clinical study on total joint replacement. In the application we consider for comparison the estimates obtained with the Fine and Gray approach (J Am Stat Assoc 94:496–509, 1999) and also time-dependent solutions of pseudo-value regression equations.     

Back propagation neural networks and multiple regressions in the case of heteroskedasticity

This paper compares the performance between regression analysis and a clustering based neural network approach when the data deviates from the homoscedasticity assumption of regression. Heteroskedasticity is a problem that arises in linear regression due to the unequal error variances. One of the methods to deal heteroskedasticity in classical regression theory is weighted least-square regression (WLS). In order to deal the problem of heteroskedasticity, backpropagation neural network is applied. In this context, an algorithm is proposed which is based on robust estimates of location and dispersion matrix that helps in preserving the error assumption of the linear regression. Analysis is carried out with appropriate designs using simulated data and the results are presented.     

An evaluation of the reconstructed coefficient of determination and potential adjustments

Previously, a method was proposed for calculating a reconstructed coefficient of determination in the case of right-censored regression using the expectation–maximization (EM) algorithm. This measure is assessed via simulation study for the purpose of evaluating the utility of model fit. Further, several reconstructed adjusted coefficients of determination are proposed and compared via simulation study for the purpose of model selection. The application of these proposed measures is illustrated on a real dataset.     

人口受教育程度对居民消费的影响研究--基于动态面板分位数回归法

本文采用1996～2015年的31个省市自治区宏观数据,使用动态面板分位数回归方法研究人口受教育程度和居民消费的数量关系。研究结果表明,人口受教育程度对消费有着较为显著的影响,且人口受教育程度对中等消费支出水平的影响略大于高、低消费支出水平的影响,这说明中等消费水平的居民消费受到人口受教育程度的影响更加敏感和有弹性。另外,模型中其他各解释变量系数在各分位数上的差异不大,说明这些影响因素对于不同消费支出水平的消费影响没有太明显差异。     

基于尾部指数回归方法的CVaR估计以及实证研究

 在险价值VaR是一种非常重要的金融风险度量方法,近期也有很多关于动态VaR以及条件VaR (CVaR) 等方面的研究。根据金融资产的收益率具有重尾特征这一事实,本文假定金融资产收益率服从重尾分布,并假定重尾分布的尾部指数随着收益率发生变化。本文基于尾部指数回归模型对重尾分布的尾部指数进行估计,进而得到收益率尾部数据所服从的条件分布,并首次运用该方法对条件VaR进行估计。本文对沪深300指数进行了实证研究,得到CVaR的估计,并对估计得到的CVaR的预测效果作出检验,并与传统VaR估计方法进行了对比,实证结果发现本文的方法的预测效果更好。     

FDI Determinants: Case of Romania

Even if the FDI is important for all host countries, for those in the process of transition to a market economy the FDI presence is critical under many respects. Not all transition countries benefited from the very beginning from the FDI presence. Several determinant factors explain the differences. Romania was lagging behind regarding the interest of foreign investors during the first 9–10 years of transition. The situation has improved greatly. The aim of this paper is to identify the main factors determining the evolution in the FDI/GDP (%) as proxy for the FDI evolution. To this end, we used the method of factors analyses. The four resulted determinant factors are: Market size and potential, Reform progress, Business liberalization, and Labor cost. A linear regression model expresses the connections between dependent variable and the four determinant factors. The paper concludes with certain policy implications.

A Bayesian approach to non-parametric monotone function estimation

Summary.  The paper proposes two Bayesian approaches to non-parametric monotone function estimation. The first approach uses a hierarchical Bayes framework and a characterization of smooth monotone functions given by Ramsay that allows unconstrained estimation. The second approach uses a Bayesian regression spline model of Smith and Kohn with a mixture distribution of constrained normal distributions as the prior for the regression coefficients to ensure the monotonicity of the resulting function estimate. The small sample properties of the two function estimators across a range of functions are provided via simulation and compared with existing methods. Asymptotic results are also given that show that Bayesian methods provide consistent function estimators for a large class of smooth functions. An example is provided involving economic demand functions that illustrates the application of the constrained regression spline estimator in the context of a multiple-regression model where two functions are constrained to be monotone.     

A Critical Look at Some Analyses of Major League Baseball Salaries

At a data analysis exposition sponsored by the Section on Statistical Graphics of the ASA in 1988, 15 groups of statisticians analyzed the same data about salaries of major league baseball players. By examining what they did, what worked, and what failed, we can begin to learn about the relative strengths and weaknesses of different approaches to analyzing data. The data are rich in difficulties. They require reexpression, contain errors and outliers, and exhibit nonlinear relationships. They thus pose a realistic challenge to the variety of data analysis techniques used. The analysis groups chose a wide range of model-fitting methods, including regression, principal components, factor analysis, time series, and CART. We thus have an effective framework for comparing these approaches so that we can learn more about them. Our examination shows that approaches commonly identified with Exploratory Data Analysis are substantially more effective at revealing the underlying patterns in the data and at building parsimonious, understandable models that fit the data well. We also find that common data displays, when applied carefully, are often sufficient for even complex analyses such as this.     

Understanding Canonical Correlation through the General Linear Model and Principal Components

Canonical correlation has been little used and little understood, even by otherwise sophisticated analysts. An alternative approach to canonical correlation, based on a general linear multivariate model, is presented. Properties of principal component analysis are used to help explain the method. Standard computational methods for full rank canonical correlation, techniques for canonical correlation on component scores, and canonical correlation with less than full rank are discussed. They are seen to be essentially equivalent when the model equation for canonical correlation on component scores is presented. The two approaches to less than full rank situations are equivalent in some senses, but quite different in usefulness, depending on the application. An example dataset is analyzed in detail to help demonstrate the conclusions.