On Asymptotic Properties of a Maximum Likelihood Estimator of Stochastically Ordered Distribution Function

- Journal title : Communications for Statistical Applications and Methods
- Volume 20, Issue 3, 2013, pp.185-191
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2013.20.3.185

Title & Authors

On Asymptotic Properties of a Maximum Likelihood Estimator of Stochastically Ordered Distribution Function

Oh, Myongsik;

Oh, Myongsik;

Abstract

Kiefer (1961) studied asymptotic behavior of empirical distribution using the law of the iterated logarithm. Robertson and Wright (1974a) discussed whether this type of result would hold for a maximum likelihood estimator of a stochastically ordered distribution function; however, we show that this cannot be achieved. We provide only a partial answer to this problem. The result is applicable to both estimation and testing problems under the restriction of stochastic ordering.

Keywords

Law of the iterated logarithm;maximum likelihood estimation;stochastically ordered distribution function;

Language

English

References

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Kiefer, J. (1961). On large deviation of the empirical distribution function of vector random variable and a law of the iterative logarithm, Pacific Journal of Mathematics, 11, 649-660.

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4.

Robertson, T. and Wright, F. T. (1974a). On the maximum likelihood estimation of stochastically ordered random variables, The Annals of Statistics, 2, 528-534.

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Robertson, T. and Wright, F. T. (1974b). A norm reducing property for isotonized cauchy mean value functions, The Annals of Statistics, 2, 1302-1307.

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