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Error Process Indexed by Bandwidth Matrices in Multivariate Local Linear Smoothing

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Publication Date
Volume
66
Issue
2
Identifiers
DOI: 10.1006/jmva.1998.1746
Keywords
  • Bandwidth Matrix
  • Error Process
  • Local Linear Smoother
  • Multiparameter Stochastic Process
  • Nonparametric Regression
  • Tightness
  • Weak Convergence

Abstract

Abstract We focus on nonparametric multivariate regression function estimation by locally weighted least squares. The asymptotic behavior for a sequence of error processes indexed by bandwidth matrices is derived. We discuss feasible data-driven consistent estimators minimizing asymptotic mean squared error or efficient estimators reducing asymptotic bias at points where opposite sign curvatures of the regression function are present in different directions.

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