Advertisement

On stable laws for estimating functions and derived estimators

  • Pranab Kumar Sen
Article
  • 11 Downloads

Summary

Stable laws forM-estimators, maximum likelihood and other estimators and obtained through parallel results for the estimating functions and relative compactness of some related estimating functional processes.

Key words and phrases

Asymptotic distribution estimating functions M-estimators maximum likelihood estimators relative compactness stable laws 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Billingsley, P. (1968).Convergence of Probability Measures, John Wiley, New York.MATHGoogle Scholar
  2. [2]
    Chatterjee, S. D. (1969). AnL p-convergence theorem,Ann. Math. Statist.,40, 1068–1070.MathSciNetGoogle Scholar
  3. [3]
    Hájek, J. (1970). A characterization of limiting distributions of regular estimates,Zeitschrift Wahrsch. verw. Geb.,14, 323–330.MATHCrossRefGoogle Scholar
  4. [4]
    Huber, P. J. (1967). The behaviour of maximum likelihood estimators under nonstandard conditions,Proc. Fifth Berkeley Symp. Math. Statist. Prob.,1, 221–233.MATHMathSciNetGoogle Scholar
  5. [5]
    Inagaki, N. (1970). On the limiting distribution of a sequence of estimators with uniformity property,Ann. Inst. Statist. Math.,22, 1–13.MATHMathSciNetGoogle Scholar
  6. [6]
    Inagaki, N. (1973). Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator,Ann. Inst. Statist. Math.,25, 1–26.MATHMathSciNetGoogle Scholar
  7. [7]
    Jurečková, J. and Sen, P. K. (1981a). Invariance principles for some stochastic processes related toM-estimators and their role in sequential statistical inference,Sankhyã, Ser. A,43, 191–210.Google Scholar
  8. [8]
    Jurečková, J. and Sen, P. K. (1981b). Sequential procedures based onM-estimators with discontinuous score functions,Jour. Statist. Plan. Infer.,5, 253–266.Google Scholar

Copyright information

© Kluwer Academic Publishers 1986

Authors and Affiliations

  • Pranab Kumar Sen
    • 1
  1. 1.University of North CarolinaChapel Hill

Personalised recommendations