Universally consistent regression function estimation using hierarchial B-splines

JOURNAL OF MULTIVARIATE ANALYSIS

卷:68

Article

Kohler, M

关键词: data-dependent partitions;    integrated squared error;    least squares estimate;    polynomial splines;    regression estimate;    universal consistency;   

DOI  :  10.1006/jmva.1998.1782

来源: Elsevier

【 摘 要 】

Estimation of multivariate regression functions from i.i.d. data is considered. We construct estimates by empirical L-2-error minimization over data-dependent spaces of polynomial spline functions. For univariate regression function estimation these spacer are spline spaces with data-dependent knot sequences. In the multivariate case, we use so-called hierarchical spline spaces which are defined as linear span of tensor product B-splines with nested knot sequences, The knot sequences of the chosen B-splines depend locally on the data. We show the strong L-2-consistency of the estimators without any condition on the underlying distribution. The estimators are similar to histogram regression estimators using data-dependent partitions and partitioning regression estimators based on local polynomial fits. The main difference is that the estimators considered here are smooth functions, which seems to be desirable especially in the case that the regression function to be estimated is smooth. (C) 1999 Academic Press.

【 授权许可】

Free