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On Limited Dependent Variable Models:Maximum Likelihood Estimation and Test of One-sidedHypothesis

Published online by Cambridge University Press:  11 February 2009

Mervyn J. Silvapulle
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Abstract

The limited dependent variable models with errorshaving log-concave density functions are studiedhere. For such models with normal errors, theasymptotic normality of the maximum likelihoodestimator was established by Amemiya [1]. We show,when the density of the error distribution islog-concave, that the maximum likelihood estimatorexists with arbitrarily large probability for largesample sizes, and is asymptotically normal. Thegeneral theory presented here includes the importantspecial cases of normal, logistic, and extreme valueerror distributions. The main results areestablished under rather weak conditions. It is alsoshown that, under the null hypothesis, theasymptotic distribution of the likelihood ratiostatistic for testing a one-sided alternativehypothesis is a weighted sum of chi-squares.

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Type
Research Article
Information
Econometric Theory , Volume 7 , Issue 3 , September 1991 , pp. 385 - 395
Copyright
Copyright © Cambridge University Press 1991

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References

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