Skip to main content
SpringerLink
Log in

Existence theorems of a maximum likelihood estimate from a generalized censored data sample

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

A new type of random sample, called a generalized censored data sample, is defined. An approach to finding criteria for the existence of a maximum likelihood estiamte from a finite generalized censored data sample is presented. This approach, named the probability contents boundary analysis, gives systematically a number of practical criteria, each of which is effective for various kinds of typical distribution families in statistical analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Boag, J. W. (1949). Maximum likelihood estimates of the proportionof patients cured by cancer therapy,J. R. Statist. Soc., B,11, 15–53.

    MATH  Google Scholar 

  2. Bourbaki, N. (1965).Topologie générale, Chap. 1 et 2, Hermann, Paris.

    Google Scholar 

  3. Carter, W. H., Jr., Bowen, J. V., Jr. and Myers, R. H. (1971). Maximum likelihood estimation from grouped Poisson data,J. Amer. Statist. Ass.,66, 351–353.

    Article  Google Scholar 

  4. Kariya, T. and Nakamura, T. (1978). The maximum likelihood estimates based on the incomplete quantal response data,J. Japan. Statist. Soc.,8, 21–28.

    MathSciNet  Google Scholar 

  5. Kariya, T. (1981). Statistical analysis of the interval-censored sample,J. Japan Statist. Soc.,11, 143–160.

    MathSciNet  MATH  Google Scholar 

  6. Kulldorff, G. (1957). On the conditions for consistency and asymptotic efficiency of maximum likelihood estimates,Skand. Aktuarietidskr.,40, 129–144.

    MathSciNet  MATH  Google Scholar 

  7. Kulldorff, G. (1962).Contributions to the Theory of Estimation from Grouped and Partially Grouped Samples, John Wiley and Sons, New York.

    Google Scholar 

  8. Moran, P. A. P. (1966). Estimation from inequalities,Aust. J. Statist.,8, 1–8.

    Article  Google Scholar 

  9. Nabeya, S. (1983). Maximum likelihood estimation from interval data (in Japanese),Japanese J. Appl. Statist.,12, 59–67.

    Article  Google Scholar 

  10. Nakamura, T. and Kariya, T. (1975). On the weighted least squares estimation and the existence theorem of its optimal solution,Kawasaki Medical J (Liberal Arts and Science Course),1, 1–11.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kawasaki Medical School, Kawasaki, Japan

    Tadashi Nakamura

Authors
  1. Tadashi Nakamura
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Nakamura, T. Existence theorems of a maximum likelihood estimate from a generalized censored data sample. Ann Inst Stat Math 36, 375–393 (1984). https://doi.org/10.1007/BF02481977

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02481977

Key words

Search

Navigation