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 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.