Likelihood-Based Local Polynomial Fitting for Single-Index Models
AbstractThe parametric generalized linear model assumes that the conditional distribution of a response Y given a d-dimensional covariate X belongs to an exponential family and that a known transformation of the regression function is linear in X. In this paper we relax the latter assumption by considering a nonparametric function of the linear combination [beta]TX, say [eta]0([beta]TX). To estimate the coefficient vector [beta] and the nonparametric component [eta]0 we consider local polynomial fits based on kernel weighted conditional likelihoods. We then obtain an estimator of the regression function by simply replacing [beta] and [eta]0 in [eta]0([beta]TX) by these estimators. We derive the asymptotic distributions of these estimators and give the results of some numerical experiments.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 80 (2002)
Issue (Month): 2 (February)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-30, November.
- Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
- Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Rank-based inference for the single-index model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 535-541.
- Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
- Huh, Jib, 2012. "Nonparametric estimation of the regression function having a change point in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 843-851.
- Park, Cheolwoo & Huh, Jib, 2013. "Statistical inference and visualization in scale-space using local likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 336-348.
If references are entirely missing, you can add them using this form.