Stochastic correlation coefficient ensembles for variable selection

In this paper, we propose a novel Max-Relevance and Min-Common-Redundancy criterion for variable selection in linear models. Considering that the ensemble approach for variable selection has been proven to be quite effective in linear regression models, we construct a variable selection ensemble (VSE) by combining the presented stochastic correlation coefficient algorithm with a stochastic stepwise algorithm. We conduct extensive experimental comparison of our algorithm and other methods using two simulation studies and four real-life data sets. The results confirm that the proposed VSE leads to promising improvement on variable selection and regression accuracy.     

Regression for non-Euclidean data using distance matrices

Regression methods for common data types such as measured, count and categorical variables are well understood but increasingly statisticians need ways to model relationships between variable types such as shapes, curves, trees, correlation matrices and images that do not fit into the standard framework. Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the responses can be developed using standard methods. We call scoring as the transformation from a new observation to a score, whereas backscoring is a method to represent a score as an observation in the data space. Both methods are essential for prediction and explanation. We illustrate the methodology for shape data, unregistered curve data and correlation matrices using motion capture data from an experiment to study the motion of children with cleft lip.     

The eigenstructure of block-structured correlation matrices and its implications for principal component analysis

Block-structured correlation matrices are correlation matrices in which the p variables are subdivided into homogeneous groups, with equal correlations for variables within each group, and equal correlations between any given pair of variables from different groups. Block-structured correlation matrices arise as approximations for certain data sets’ true correlation matrices. A block structure in a correlation matrix entails a certain number of properties regarding its eigendecomposition and, therefore, a principal component analysis of the underlying data. This paper explores these properties, both from an algebraic and a geometric perspective, and discusses their robustness. Suggestions are also made regarding the choice of variables to be subjected to a principal component analysis, when in the presence of (approximately) block-structured variables.     

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.     

Tables of the exact quantiles of the top-down correlation coefficient for n - 3(1)14

Iman and Connver (1985, 1987) have suggested the top-down correlation coefficient as a measure of association when n objects are ranked by two or more independent sources and interest centers primarily on agreement in the top rankings, with disagreements on items at the bottom of the rankings being of little or no importance. The top-down correlation coefficient results from computing the ordinary Pearson correlation coefficient on Savage scores. Quantiles of the exact distribution of the top-down correlation coefficient based on the assumption of independent rankings are provided for n = 3(1)14.     

Weighted Stochastic Restricted Estimation in Linear Measurement Error Models

This article discusses the consistent estimation of the parameters in a linear measurement error model when stochastic linear restrictions on regression coefficients are available. We propose some methodologies to obtain the consistent estimation when either the covariance matrix of the measurement errors or the reliability matrix of independent variables is known. Their finite- and large-sample properties are derived with not necessarily normal errors. A Monte Carlo simulation is carried out to study the the finite properties of the estimators.     

Finding environmentally important industry clusters: Multiway cut approach using nonnegative matrix factorization

This paper proposes an optimal combinatorial method for finding groups of industries with relatively large CO₂ emissions through industrial relations. Using an economic input–output table, we estimated a non-symmetric matrix describing how much CO₂ is emitted in producing the commodity of industry i, which was purchased to produce commodity of industry j, to meet the final demand for a specific commodity. A symmetric strength of relations matrix describing the CO₂ emissions associated with the industrial relations was further estimated using the non-symmetric matrix. The strength of relations matrix can be viewed as a representation of the supply-chain network of the final commodity. In this study, we estimated the strength of relations matrix associated with the final demand for automobiles and applied the multiway cut approach using nonnegative matrix factorization to the matrix in order to find environmentally important industry clusters in the Japanese automobile supply chain. According to our empirical results, the optimal number of industry clusters is 19, and 4 industry clusters are playing a key role in CO₂ emission reduction.     

A robust procedure for testing an assumed value of the population correlation coefficient

For testing that the population correlations coefficientp Q, Tiku and Balakrishnan1986) developed a robust test. This test is extended here to situcitions where one wants to test that p p , p being a specified non-zero value of p. o o