A Simple Consistent Non-parametric Estimator of the Regression Function in a Truncated Sample
AbstractMuch recent work has focused on the estimation of regression functions in samples which are truncated or censored. Much of this work has focused on the estimation of a parametric regression function with an error distribution of unknown form. While these method relax a strong parametric assumption about which we seldom have a priori information, they still impose a strong parametric assumption on the regression equation (which is presumably the focus of the analysis). Here we take the other approach. An estimator is proposed for the problem of non-parametric regression when the sample is truncated above or below some known threshold of the dependent variable. We specify the error distribution up to a vector of parameters while estimating the regression function without assuming a parametric form. A simple ``backfit'' estimator based on an initial kernel smooth is proposed. We establish consistency results for this estimator when the error distribution is known up to a finite parameter vector and satisfies some regularity conditions. A small monte-carlo study is performed to ascertain the finite sample properties of the estimator. The estimator is found to perform well in our experiment: achieving reasonableaverage absolute errors relative to the maximum likelihood estimator- especially when truncation is severe.
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 InfoPaper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0651.
Date of creation: 01 Aug 2000
Date of revision:
Contact details of provider:
Phone: 1 212 998 3820
Fax: 1 212 995 4487
Web page: http://www.econometricsociety.org/pastmeetings.asp
More information through EDIRC
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.:
- Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
- Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
- Newey, Whitney K., 1986. "Linear instrumental variable estimation of limited dependent variable models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 32(1), pages 127-141, June.
- Ruud, Paul A., 1986. "Consistent estimation of limited dependent variable models despite misspecification of distribution," Journal of Econometrics, Elsevier, vol. 32(1), pages 157-187, June.
- Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
- Lee, Lung-fei, 1994.
"Semiparametric two-stage estimation of sample selection models subject to Tobit-type selection rules,"
Journal of Econometrics,
Elsevier, vol. 61(2), pages 305-344, April.
- Lee, L-F., 1990. "Semiparametric Two Stage Estimation of Sample Selection Models Subject to Tobit-Type Selection Rules," Papers 256, Minnesota - Center for Economic Research.
- Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
- Fernandez, Luis, 1986. "Non-parametric maximum likelihood estimation of censored regression models," Journal of Econometrics, Elsevier, vol. 32(1), pages 35-57, June.
- Goldberger, Arthur S., 1981. "Linear regression after selection," Journal of Econometrics, Elsevier, vol. 15(3), pages 357-366, April.
- Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
- Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-60, November.
- Horowitz, Joel L., 1986. "A distribution-free least squares estimator for censored linear regression models," Journal of Econometrics, Elsevier, vol. 32(1), pages 59-84, June.
- Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
- Duncan, Gregory M., 1986. "A semi-parametric censored regression estimator," Journal of Econometrics, Elsevier, vol. 32(1), pages 5-34, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If references are entirely missing, you can add them using this form.