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UNCONSTRAINED PILOT SELECTORS FOR SMOOTHED CROSS‐VALIDATION
Author(s) -
Chacón José E.,
Duong Tarn
Publication year - 2011
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2011.00639.x
Subject(s) - cross validation , bandwidth (computing) , mathematics , algorithm , scalar (mathematics) , mathematical optimization , selection (genetic algorithm) , matrix (chemical analysis) , flexibility (engineering) , computer science , statistics , machine learning , computer network , materials science , geometry , composite material
Summary Two of the most useful multivariate bandwidth selection techniques are the plug‐in and cross‐validation methods. The smoothed version of the cross‐validation method is known to reduce the variability of its non‐smoothed counterpart; however, it shares with the plug‐in choice the need for a pilot bandwidth matrix. Owing to the mathematical difficulties encountered in the optimal pilot choice, it is common to restrict this pilot matrix to be a scalar multiple of the identity matrix, at the expense of losing the flexibility afforded by the unconstrained approach. Here we show how to overcome these difficulties and propose a smoothed cross‐validation selector using an unconstrained pilot matrix. Our numerical results indicate that the unconstrained selector outperforms the constrained one in practice, and is a viable competitor to unconstrained plug‐in selectors.