Abstract
Censored regression (“Tobit”) models have been in common use, and their linear hypothesis testings have been widely studied. However, the critical values of these tests are usually related to quantities of an unknown error distribution and estimators of nuisance parameters. In this paper, we propose a randomly weighting test statistic and take its conditional distribution as an approximation to null distribution of the test statistic. It is shown that, under both the null and local alternative hypotheses, conditionally asymptotic distribution of the randomly weighting test statistic is the same as the null distribution of the test statistic. Therefore, the critical values of the test statistic can be obtained by randomly weighting method without estimating the nuisance parameters. At the same time, we also achieve the weak consistency and asymptotic normality of the randomly weighting least absolute deviation estimate in censored regression model. Simulation studies illustrate that the performance of our proposed resampling test method is better than that of central chi-square distribution under the null hypothesis.
Similar content being viewed by others
References
Powell J L. Least absolute deviations estimation for the censored regression model. J Econometrics, 25: 303–325 (1984)
Huber P J. The behaviour of maximum likelihood estimates under nonstandard conditions. In: Proc Fifth Berkeley Symp Math Statist Probab, Vol. 1. Berkeley: University of California Press, 1967, 221–233
Pollard D. Empirical Process: Theory and Application. NSF-CBMS Regional Conference Series in Probability and Statistics, Vol. 2. Hayward: Institute of Mathematical Statistics, 1990
Chen X R, Wu Y. Consistency of L 1 estimates in censored linear regression models. Comm Statist Theory Methods, 23(7): 1847–1858 (1993)
Rao C R, Zhao L C. Asymptotic normality of LAD estimator in censored regression models. Math Methods Statist, 2: 228–239 (1993)
Zhao L C, Fang Y X. Random weighting method for censored regression model. J Syst Sci Complex, 17(2): 262–270 (2004)
Fang Y X, Jin M, Zhao L C. Strong convergance of LAD estimates in a censored regression model. Sci China Ser A-Math, 48(2): 155–168 (2005)
Zhao L C. Linear hypothesis testing in censored regression models. Statist Sinica, 14: 333–347 (2004)
Rao C R, Zhao L C. Approximation to the distribution of M-estimates in linear models by randomly weighted bootstrap. Sankhya, 54(3): 323–331 (1992)
Chen K N, Ying Z L, Zhao L C. Analysis of least absolute deviation. Biometrika, 95(1): 107–122 (2008)
Bennett G. Probality inequalities for the sum of independent random variables. J Amer Statist Assoc, 57: 33–45 (1962)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by National Natural Science Foundation of China (Grant No. 10471136), PhD Program Foundation of the Ministry of Education of China, and Special Foundations of the Chinese Academy of Sciences and University of Science and Technology of China
Rights and permissions
About this article
Cite this article
Wang, Z., Wu, Y. & Zhao, L. Approximation by randomly weighting method in censored regression model. Sci. China Ser. A-Math. 52, 561–576 (2009). https://doi.org/10.1007/s11425-008-0116-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-008-0116-x
Keywords
- censored regression model
- least absolute deviation
- asymptotic normality
- local alternative
- randomly weighting method
- asymptotic power