Abstract
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 language | English |
---|---|
Pages (from-to) | 343-351 |
Number of pages | 9 |
Journal | Journal of Statistical Planning and Inference |
Volume | 107 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 1 Sept 2002 |
Externally published | Yes |
Keywords
- Asymptotic normality
- Brownian motion
- Convex minorant
- Isotonic regression
- Semiparametric model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics