Department of Economics and Business Economics

Nonparametric kernel regression with multiple predictors and multiple shape constraints

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  • Peng Du, Confucius Institute for Innovation and Learning, Denmark
  • C.F. Parmeter, University of Miami
  • ,
  • J.S. Racine
Nonparametric smoothing under shape constraints has recently received much well-deserved attention. Powerful methods have been proposed for imposing a single shape constraint such as monotonicity and concavity on univariate functions. In this paper, we extend the monotone kernel regression method in Hall and Huang (2001) to the multivariate and multi-constraint setting. We impose equality and/or inequality constraints on a nonparametric kernel regression model and its derivatives. A bootstrap procedure is also proposed for testing the validity of the constraints. Consistency of our constrained kernel estimator is provided through an asymptotic analysis of its relationship with the unconstrained estimator. Theoretical underpinnings for the bootstrap procedure are also provided. Illustrative Monte Carlo results are presented and an application is considered.
Original languageEnglish
JournalStatistica Sinica
Pages (from-to)1347-1371
Number of pages25
Publication statusPublished - 1 Jul 2013

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