Science in China Series A: Mathematics

, Volume 45, Issue 11, pp 1398–1407 | Cite as

Convergence rates of MLE in a partly linear model



This paper considers the estimation for a partly linear model with case 1 interval censored data. We assume that the error distribution belongs to a known family of scale distributions with an unknown scale parameter. The sieve maximum likelihood estimator (MLE) for the model’s parameter is shown to be strongly consistent, and the convergence rate of the estimator is obtained and discussed.


partly linear model case 1 interval censored data sieve MLE strong consistency convergence rate 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Engle, R. F., Granger, C. W. J., Rice, J. et al., Semiparametric estimates of the relation between weather and electricity sales, Journal of the American Statistical Association, 1986, 81: 310–320.CrossRefGoogle Scholar
  2. 2.
    Chen, H., Convergence rates for parametric components in a partly linear model, Annals of Statistics, 1988, 16: 136–146.CrossRefMathSciNetMATHGoogle Scholar
  3. 3.
    Wang, Q. H., Zheng, Z. G., Asymptotic properties for the semiparametric regression model with randomly censored data, Science in China, Ser. A, 1997, 40(9): 945–957.CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Xue, H. Q., Song, L. X, Li, G. Y., Sieve MLE for partly linear model with case 1 interval censoring, Acta Mathematicae Applicatae Sinica (in Chinese), 2001, 24: 139–151.MathSciNetMATHGoogle Scholar
  5. 5.
    Shen, X., Wong, W. H., Convergence rate of sieve estimates, Annals of Statistics, 1994, 22: 580–615.CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    Wong, W. H., Shen, X., Probability inequalities for likelihood ratios and convergence rates of maximum likelihood estimate, Annals of Statistics, 1995, 23: 339–362.CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    Ossiander, M., A central limit theorem under metric entropy with L2 bracketing, Annals of Probability, 1997, 15: 897–919.CrossRefMathSciNetGoogle Scholar
  8. 8.
    Pollard, D., Empirical Processes: Theory and Applications, NSF-CBMS Regional Conference Series in Probability and Statistics 2, Hayward: Institute of Mathematical Statistics, 1990.Google Scholar
  9. 9.
    Pollard, D., Convergence of Stochastic Processes, New York: Springer-Verlag, 1984.MATHGoogle Scholar
  10. 10.
    Huang, J., Efficient estimation for the proportional hazards model with interval censoring, Annals of Statistics, 1996, 24: 540–568.CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Science in China Press 2002

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate SchoolChinese Academy of SciencesBeijingChina

Personalised recommendations