Halton and Hammersley sequences in multivariate nonparametric regression

The present paper generalizes results by Rafajłowicz and Schwabe [2003. Equidistributed designs in nonparametric regression. Statist. Sinica 13, 129–142] for quasi least squares estimators in additive regression to a general multivariate regression setup. Equidistributed sequences of Halton or Hamme...

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Bibliographic Details
Published in:Statistics & probability letters 2006-04, Vol.76 (8), p.803-812
Main Authors: Rafajłowicz, Ewaryst, Schwabe, Rainer
Format: Article
Language:English
Subjects:
Exact sciences and technology
Experimental design
Experimental design Nonparametric regression Quasi-random sequences
Mathematics
Nonparametric inference
Nonparametric regression
Probability and statistics
Quasi-random sequences
Sciences and techniques of general use
Statistics
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Summary:The present paper generalizes results by Rafajłowicz and Schwabe [2003. Equidistributed designs in nonparametric regression. Statist. Sinica 13, 129–142] for quasi least squares estimators in additive regression to a general multivariate regression setup. Equidistributed sequences of Halton or Hammersley type provide consistent regression estimators with a satisfactory rate of convergence. As those sequences are easy to construct they can serve as suitable experimental designs. Optimal generators for the Halton and Hammersley sequences are found by exhaustive search.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2005.10.014