Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions

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Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions

Author Info

Newey, Whitney K.
Powell, James L.

Abstract

We consider the linear regression model with censored dependent variable, where the disturbance terms are restricted only to have zero conditional median (or other prespecified quantile) given the regressors and the censoring point. Thus, the functional form of the conditional distribution of the disturbances is unrestricted, permitting heteroskedasticity of unknown form. For this model, a lower bound for the asymptotic covariance matrix for regular estimators of the regression coefficients is derived. This lower bound corresponds to the covariance matrix of an optimally weighted censored least absolute deviations estimator, where the optimal weight is the conditional density at zero of the disturbance. We also show how an estimator that attains this lower bound can be constructed, via nonparametric estimation of the conditional density at zero of the disturbance. As a special case our results apply to the (uncensored) linear model under a conditional median restriction.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 6 (1990)
Issue (Month): 03 (September)
Pages: 295-317
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:cup:etheor:v:6:y:1990:i:03:p:295-317_00

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Sun, Y., 2003. "Square Root N - Consistent Semiparametric Estimation of Partially Linear Quantile Regression Models," Working Papers 2003-11, University of Guelph, Department of Economics. [Downloadable!]
Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society. [Downloadable!]
Other versions:
- Robert Engle & Simone Manganelli, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series 1999-20, Department of Economics, UC San Diego. [Downloadable!]
- Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series 99-20, Department of Economics, UC San Diego. [Downloadable!]
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Andrew Chesher, 2002. "Instrumental Values," CeMMAP working papers CWP17/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Other versions:
- Chesher, Andrew, 2007. "Instrumental values," Journal of Econometrics, Elsevier, vol. 139(1), pages 15-34, July. [Downloadable!] (restricted)
Lingjie Ma & Roger Koenker, 2004. "Quantile regression methods for recursive structural equation models," CeMMAP working papers CWP01/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
Other versions:
- Ma, Lingjie & Koenker, Roger, 2006. "Quantile regression methods for recursive structural equation models," Journal of Econometrics, Elsevier, vol. 134(2), pages 471-506, October. [Downloadable!] (restricted)
Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
Sun, Y., 2003. "A Consistent Nonparametric Equality Test of Conditional Quantile Functions," Working Papers 2003-10, University of Guelph, Department of Economics. [Downloadable!]
Other versions:
- Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(04), pages 614-632, August. [Downloadable!]
Moshe Buchinsky & Jinyong Hahn, . "Quantile Regression Model with Unknown Censoring," Working Papers _004, University of California at Berkeley, Econometrics Laboratory Software Archive. [Downloadable!]
Andrew Chesher, 2001. "Exogenous impact and conditional quantile functions," Econometrics 0108001, EconWPA. [Downloadable!]
Other versions:
- Andrew Chesher, 2001. "Exogenous impact and conditional quantile functions," CeMMAP working papers CWP01/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]

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