Abstract
We consider the progressively truncated estimating functions and estimators as a generalization of the progressively truncated likelihood estimating functions and maximum likelihood estimators. We show the uniform consistency and weak convergence of the progressively truncated estimators.
Similar content being viewed by others
References
Chernoff H. and Rubin H. (1956) The estimation of the location of a discontinuity in density, Proc. of the Third Berkeley Symp. Math. Statist. Prob., Vol. 1, 19–37.
Huber P. J. (1967). The behavior of maximum likelihood estimators under nonstandard conditions, Proc. of the Fifth Berkeley Symp. Math. Statist. Prob., Vol. 1, 221–233.
Inagaki N. (1973). Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator, Ann. Inst. Statist. Math., 25, 1–26.
Inagaki N. and Sen P. K. (1985). On progressively truncated maximum likelihood estimators, Ann. Inst. Statist. Math., 37, 251–269.
Karlin, S. and Taylor, H. M. (1981). A First Course in Stochastic Process, 2nd ed., Academic Press.
Lawless J. F. (1982). Statistical Models and Methods for Lifetime Data, Wiley, New York.
Sen P. K. (1976). Weak convergence of progressively censored likelihood ratio statistics and its role in asymptotic theory of life testing, Ann. Statist., 4, 1247–1257.
Sen P. K. (1981). Sequential Nonparametrics, Wiley, New York.
Sen P. K. and Tsong Y. (1981). An invariance principle for progressively truncated likelihood ratio statistics, Metrika, 28, 165–177.
Author information
Authors and Affiliations
About this article
Cite this article
Inagaki, N. The progressively truncated estimating functions and estimators. Ann Inst Stat Math 40, 521–540 (1988). https://doi.org/10.1007/BF00053063
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00053063