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

  • Tadashi Nakamura


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.

Key words

Existence of a maximum likelihood estimate generalized censored data sample global maximum maximum likelihood estimate 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Boag, J. W. (1949). Maximum likelihood estimates of the proportionof patients cured by cancer therapy,J. R. Statist. Soc., B,11, 15–53.zbMATHGoogle Scholar
  2. [2]
    Bourbaki, N. (1965).Topologie générale, Chap. 1 et 2, Hermann, Paris.Google Scholar
  3. [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.CrossRefGoogle Scholar
  4. [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.MathSciNetGoogle Scholar
  5. [5]
    Kariya, T. (1981). Statistical analysis of the interval-censored sample,J. Japan Statist. Soc.,11, 143–160.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Kulldorff, G. (1957). On the conditions for consistency and asymptotic efficiency of maximum likelihood estimates,Skand. Aktuarietidskr.,40, 129–144.MathSciNetzbMATHGoogle Scholar
  7. [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. [8]
    Moran, P. A. P. (1966). Estimation from inequalities,Aust. J. Statist.,8, 1–8.CrossRefGoogle Scholar
  9. [9]
    Nabeya, S. (1983). Maximum likelihood estimation from interval data (in Japanese),Japanese J. Appl. Statist.,12, 59–67.CrossRefGoogle Scholar
  10. [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.CrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1984

Authors and Affiliations

  • Tadashi Nakamura
    • 1
  1. 1.Kawasaki Medical SchoolKawasakiJapan

Personalised recommendations