Approximation to the distribution of LAD estimators for censored regression by random weighting method. (English) Zbl 1156.62347
Summary: J. L. Powell [J. Econ. 25, 303–325 (1984; Zbl 0571.62100)] considered a 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 earlier papers, this difficulty may be solved by applying the bootstrap method [see, e.g., J. Hahn, J. Econ. Theory 11, 105–121 (1995); Y. Bilias et al., J. Econ. 99, No. 2, 373–386 (2000; Zbl 1076.62567)]. We propose a random weighting method to approximate the distribution of the LAD estimator. The random weighting method was developed by D. B. Rubin [Ann. Stat. 9, 130–134 (1981)], A. Y. Lo [Ann. Stat. 15, 360–375 (1987; Zbl 0617.62032)], and D. Tu and Z. Zheng [Chin. J. Appl. Probab. Stat. 3, No. 4, 340–347 (1987; Zbl 0661.62013)], with reference to some statistics such as the sample mean. C. R. Rao and L. C. Zhao [Sankyā, Ser. A 54, No. 3, 323–331 (1992; Zbl 0773.62010)] applied the random weighting method to approximate the asymptotic distribution of M-estimators in regression models. We extend this method to the censored regression model.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62N01 | Censored data models |
| 62E20 | Asymptotic distribution theory in statistics |
| 90C90 | Applications of mathematical programming |
Software:
bootstrapReferences:
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