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

Published online by Cambridge University Press:  11 February 2009

Mervyn J. Silvapulle
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Abstract

The limited dependent variable models with errors having log-concave density functions are studied here. For such models with normal errors, the asymptotic normality of the maximum likelihood estimator was established by Amemiya [1]. We show, when the density of the error distribution is log-concave, that the maximum likelihood estimator exists with arbitrarily large probability for large sample sizes, and is asymptotically normal. The general theory presented here includes the important special cases of normal, logistic, and extreme value error distributions. The main results are established under rather weak conditions. It is also shown that, under the null hypothesis, the asymptotic distribution of the likelihood ratio statistic for testing a one-sided alternative hypothesis is a weighted sum of chi-squares.

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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