 Shape restricted nonparametric regression with Bernstein polynomialsJ. Wang and S.K. Ghosh Computational Statistics & Data Analysis, 2012, vol. 56, issue 9, 2729-2741 Abstract: The objective of this article is to develop a computationally efficient estimator of the regression function subject to various shape constraints. In particular, nonparametric estimators of monotone and/or convex (concave) regression functions are obtained by using a nested sequence of Bernstein polynomials. One of the key distinguishing features of the proposed estimator is that a given shape constraint (e.g., monotonicity and/or convexity) is maintained for any finite sample size and satisfied over the entire support of the predictor space. Moreover, it is shown that the Bernstein polynomial based regression estimator can be obtained as a solution of a constrained least squares method and hence the estimator can be computed efficiently using a quadratic programming algorithm. Finally, the asymptotic properties (e.g., strong uniform consistency) of the estimator are established under very mild conditions, and finite sample properties are explored using several simulation studies and real data analysis. The predictive performances are compared with some of the existing methods. Keywords: Bernstein polynomials; Convex; Monotone; Nonparametric regression; Shape restriction (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:9:p:2729-2741 DOI: 10.1016/j.csda.2012.02.018 Access Statistics for this article Computational Statistics & Data Analysis is currently edited by S.P. Azen More articles in Computational Statistics & Data Analysis from Elsevier |
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