2nd Special issue on matrix computations and statistics

Jesse L. Barlow, Haesun Park, Patrick J.F. Groenen, Hongyuan Zha
2006 Computational Statistics & Data Analysis  
Editorial 2nd Special issue on matrix computations and statistics A number of interesting and important ideas have resulted from the relationship between matrix computations and statistics. Well-known examples include the solution of leastsquares problems, computation of the singular value decomposition and its generalizations, estimation of principal components, computation of canonical correlations, several cluster analysis algorithms, and the solution of total least-squares problems.
more » ... ional statistics and data analysis has published papers in matrix computations and statistics (for instance, encourages submissions in this area. A previous special issue on this area featured papers on multidimensional scaling, an application to web search engines, an algorithm for seemingly unrelated regression models, an error measurement model for motion analysis, and a survey on alternating least-squares problems (Chang and PaigeThis second special issue on matrix computations and statistics continues in this direction. It contains topics such as new data analysis models, fast computational methods, and theoretical developments using matrix computations in statistics: a new model for principal components of binary data, high-speed smoothing for large grids, a theoretical and practical comparison of canonical correlation analysis and Procrustes analysis, a generalization of constrained correspondence analysis, a new generalization of total least squares, a study of the conditions for uniqueness of estimates in three-way models, a study of the use of the modified Leverrier-Faddeev algorithm to the spectral decomposition of symmetric blockcirculant matrices, and a sensitivity analysis of the Strain criterion for multidimensional scaling. Several papers developed matrix computational algorithms that were inspired by statistical applications. Li (2004) discusses the definition and application of sign eigenvectors. Sign eigenanalysis can be applied to the development of statistical inference procedures in the 1 norm. Dax (2004) presents a method for solving a system of linear inequalities Ax b. This problem is a 1 minimization problem or 1 regression problem. Gower (2004)
doi:10.1016/j.csda.2004.08.003 fatcat:4bty4gk6g5fi3hz3fraqzm4evu