Approximation to the distribution of LAD estimators for censored regression by random weighting method

Yixin Fang, Lincheng Zhao

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Abstract

Powell (J. Econometrics 25 (1984) 303) considered censored regression model, and established the asymptotic normality of the least absolute deviation (LAD) estimator. But the asymptotic covariance matrices depend on the error density and are therefore difficult to estimate reliably. In the earlier papers, this difficulty may be solved by applying the bootstrap method (see, e.g., Hahn (J. Econometric Theory 11 (1995) 105); Bilias et al. (J. Econometrics 99 (2000) 373). In this paper we propose a random weighting method to approximate the distribution of the LAD estimator. The random weighting method was developed by Rubin (Ann. Statist. 9 (1981) 130), Lo (Ann. Statist. 15 (1987) 360), Tu and Zheng (Chinese J. Appl. Probab. Statist. 3 (1987) 340) with reference to some statistics such as the sample mean. Rao and Zhao (Sankhya 54 (1992) 323) applied random weighting method to approximate asymptotic distribution of M-estimators in regression models. In this paper we extend this method to the censored regression model.

Original languageEnglish (US)
Pages (from-to)1302-1316
Number of pages15
JournalJournal of Statistical Planning and Inference
Volume136
Issue number4
DOIs
StatePublished - Apr 1 2006
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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