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Stochastic monotonicity of the MLE of exponential mean under different censoring schemes

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Abstract

In this paper, we present a general method which can be used in order to show that the maximum likelihood estimator (MLE) of an exponential mean θ is stochastically increasing with respect to θ under different censored sampling schemes. This propery is essential for the construction of exact confidence intervals for θ via “pivoting the cdf” as well as for the tests of hypotheses about θ. The method is shown for Type-I censoring, hybrid censoring and generalized hybrid censoring schemes. We also establish the result for the exponential competing risks model with censoring.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ONT, Canada, L8S 4K1

    N. Balakrishnan

  2. Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou str., 18534, Piraeus, Greece

    G. Iliopoulos

Authors
  1. N. Balakrishnan
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  2. G. Iliopoulos
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Correspondence to G. Iliopoulos.

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Balakrishnan, N., Iliopoulos, G. Stochastic monotonicity of the MLE of exponential mean under different censoring schemes. Ann Inst Stat Math 61, 753–772 (2009). https://doi.org/10.1007/s10463-007-0156-y

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  • DOI: https://doi.org/10.1007/s10463-007-0156-y

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