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ON THE CONSTRUCTION OF BOUNDS CONFIDENCE REGIONS

Published online by Cambridge University Press:  06 June 2003

Gordon C.R. Kemp
Affiliation:
University of Essex

Abstract

We modify the procedure for constructing exact bounds confidence regions introduced by Dufour (1990, Econometrica 58, 475–494) so as to drop the requirement that the confidence regions for the nuisance parameters are marginal with respect to the parameters of interest, i.e., that they are the same for all values of the parameters of interest. We illustrate this modified procedure with an application to a dependent variable heteroskedasticity model and, using a Monte Carlo study, compare the confidence regions constructed by this procedure with asymptotically justified regions.I thank the editor and three referees for useful comments. As always, I retain responsibility for any remaining errors.

Type
Research Article
Copyright
© 2003 Cambridge University Press

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References

REFERENCES

Amemiya, T. (1973) Regression analysis when the variance of the dependent variable is proportional to the square of its expectation. Journal of the American Statistical Association 68, 928934.Google Scholar
Battese, G.E. & B.P. Bonyhady (1981) Estimation of household expenditure functions: An application of a class of heteroscedastic regression models. Economic Record 57, 8085.Google Scholar
Belyaev, Y.K. (1967) On confidence intervals and sets for various statistical models. In L.M. Le Cam & J. Neyman (eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. I, pp. 5158. Berkeley and Los Angeles: University of California Press.
Doornik, J. (1999) Object-Oriented Matrix Programming Using Ox, 3rd ed. London: Timberlake Consultants Press and Oxford (http://www.nuff.ox.ac.uk/Users/Doornik).
Dufour, J.M. (1990) Exact tests and confidence sets in linear regressions with autocorrelated errors. Econometrica 58, 475494.Google Scholar
Dufour, J.M. & J.F. Kiviet (1996) Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 3968.Google Scholar
Gourieroux, C., A. Monfort, & Q. Vuong (1995) Statistics and Econometric Models, vol. 2: Testing, Confidence Regions, Model Selection, and Asymptotic Theory. Cambridge: Cambridge University Press.
Ihaka, R. & R. Gentleman (1996) R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics 5, 299314.Google Scholar
Mood, A.M. & F.A. Graybill (1963) Introduction to the Theory of Statistics, 2nd ed. New York: McGraw-Hill.
Prais, S.J. (1953) A note on heteroscedastic errors in regression analysis. Review of the International Statistical Institute 21, 2829.Google Scholar
Prais, S.J. & H.S. Houthakker (1955) The Analysis of Family Budgets. New York: Cambridge University Press.
Theil, H. (1951) Estimates and their sampling variance of parameters of certain heteroscedastic distributions. Review of the International Statistical Institute 19, 141147.Google Scholar
Theil, H. (1971) Principles of Econometrics. New York: Wiley.