A note on estimating a partly linear model under monotonicity constraints

Jian Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

41 Citations (Scopus)


We consider asymptotic properties of the least-squares estimator of a partly linear regression model when the nonparametric component is subject to monotonicity constraints. We show that the least-squares estimator of the finite-dimensional regression coefficient is root-n consistent and asymptotically normal. We also show that the isotonic estimator of the monotone nonparametric function at a fixed point is cube root-n consistent, and apart from a scale constant, has the same limiting distribution in nonparametric monotone density estimation and isotonic regression derived by Prakasa Rao (Sankhya Ser. A 31 (1969) 23) and Brunk (In: M.L. Puri (Ed.), Nonparametric Techniques in Statistical Inference, Cambridge University Press, Cambridge, 1970).
Original languageEnglish
Pages (from-to)343-351
Number of pages9
JournalJournal of Statistical Planning and Inference
Issue number1-2
Publication statusPublished - 1 Sept 2002
Externally publishedYes


  • Asymptotic normality
  • Brownian motion
  • Convex minorant
  • Isotonic regression
  • Semiparametric model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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