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On Asymptotic Properties of a Maximum Likelihood Estimator of Stochastically Ordered Distribution Function
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 Title & Authors
On Asymptotic Properties of a Maximum Likelihood Estimator of Stochastically Ordered Distribution Function
Oh, Myongsik;
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 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
 Cited by
 References
1.
Billingsley, P. (1986). Probability and Measure, 2nd ed., Wiley, New York.

2.
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. crossref(new window)

3.
Lee, C. I. C. (1987). Maximum Likelihood Estimates for Stochastically Ordered Multinomial Populations with Fixed and Random Zeros, Foundation of Statistical Inference, (I. B. MacNeill and G. J. Umphrey eds.) 189-197.

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. crossref(new window)

5.
Robertson, T. and Wright, F. T. (1974b). A norm reducing property for isotonized cauchy mean value functions, The Annals of Statistics, 2, 1302-1307. crossref(new window)

6.
Robertson, T. and Wright, F. T. (1981). Likelihood ratio tests for and against a stochastic ordering between multinomial populations, The Annals of Statistics, 9, 1248-1257. crossref(new window)

7.
Robertson, T., Wright, F. T. and Dykstra, R. L. (1988). Order Restricted Statistical Inference, Wiley, Chichester.