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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

REFERENCES

1. Amemiya, T. Regression analysis when the dependent variable is truncated normal. Econometrica 41 (1973): 997–1016.CrossRefGoogle Scholar
2. Amemiya, T. Tobit models: a survey. Journal of Econometrics 24 (1984): 3–61.CrossRefGoogle Scholar
3. Brown, B.M. Multiparameter linearization theorems. The Journal of the Royal Statistical Society, Series B 47 (1985): 323–331.Google Scholar
4. Judge, G.G. & Yancey, T.A.. Improved Methods of Inference in Econometrics. North Holland: Amsterdam, 1986.Google Scholar
5. Kodde, D.A. & Palm, F.C.. Wald criteria for jointly testing equality and inequality restrictions. Econometrica 54 (1986): 1243–1248.10.2307/1912331CrossRefGoogle Scholar
6. Maddala, G.S. Limited-Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press, 1983.CrossRefGoogle Scholar
7. Phillips, P.C.B. & Park, J.Y.. On the formulation of Wald tests of non-linear restrictions. Econometrica 56(,(1988): 1065–108310.2307/1911359Google Scholar
8. Rao, C.R. Linear Statistical Inference and Its Applications, 2nd ed. New York: Wiley, 1973.CrossRefGoogle Scholar
9. Silvapulle, M.J. On the existence of maximum likelihood estimators for the binomial response models. The Journal of the Royal Statistical Society, Series B 43 (1981): 310–313.Google Scholar
10. Silvapulle, M.J. Asymptotic behavior of robust estimators of regression and scale parameters with fixed carriers. The Annals of Statistics 13 (1985): 1490–1497.10.1214/aos/1176349750CrossRefGoogle Scholar
11. Silvapulle, M.J. & Burridge, J.. Existence of maximum likelihood estimates in regression models for grouped and ungrouped data. The Journal of the Royal Statistical Society, Series B 48 (1986): 100–106.Google Scholar
12.Vaeth, M. On the use of Wald's test in exponential families. International Statistical Review 53 (1985): 199–214.CrossRefGoogle Scholar
13.Wolak, F.A. An exact test for multiple inequality and equality constraints in the linear model. Journal of the American Statistical Association 82 (1987): 782–793.10.1080/01621459.1987.10478499Google Scholar
14. Wolak, F.A. Local and global testing of linear and nonlinear inequality constraints in nonlinear econometric models. Econometric Theory 5 (1989): 1–35.10.1017/S0266466600012238CrossRefGoogle Scholar