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Location estimation in nonparametric regression with censored data

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  • Heuchenne, Cédric
  • Van Keilegom, Ingrid

Abstract

Consider the heteroscedastic model Y=m(X)+[sigma](X)[var epsilon], where [var epsilon] and X are independent, Y is subject to right censoring, m(·) is an unknown but smooth location function (like e.g. conditional mean, median, trimmed mean...) and [sigma](·) an unknown but smooth scale function. In this paper we consider the estimation of m(·) under this model. The estimator we propose is a Nadaraya-Watson type estimator, for which the censored observations are replaced by 'synthetic' data points estimated under the above model. The estimator offers an alternative for the completely nonparametric estimator of m(·), which cannot be estimated consistently in a completely nonparametric way, whenever high quantiles of the conditional distribution of Y given X=x are involved. We obtain the asymptotic properties of the proposed estimator of m(x) and study its finite sample behaviour in a simulation study. The method is also applied to a study of quasars in astronomy.

Suggested Citation

  • Heuchenne, Cédric & Van Keilegom, Ingrid, 2007. "Location estimation in nonparametric regression with censored data," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1558-1582, September.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:8:p:1558-1582
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    References listed on IDEAS

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    1. Ingrid Van Keilegom & Noël Veraverbeke, 1997. "Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 467-491, September.
    2. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    3. Cédric Heuchenne & Ingrid Keilegom, 2007. "Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 273-297, June.
    4. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    5. Songnian Chen & Gordon B. Dahl & Shakeeb Khan, 2005. "Nonparametric Identification and Estimation of a Censored Location-Scale Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 212-221, March.
    6. Gang Li & Somnath Datta, 2001. "A Bootstrap Approach to Nonparametric Regression for Right Censored Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 708-729, December.
    7. Portnoy S., 2003. "Censored Regression Quantiles," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1001-1012, January.
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