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Nonparametric Regression Tests Based on Least Squares

Published online by Cambridge University Press:  18 October 2010

Adonis John Yatchew
Adonis John Yatchew
Affiliation:
University of Toronto
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Abstract

This paper proposes tests on semiparametric models based on the sum of squared residuals from a least-squares procedure. Smoothness conditions are imposed on the nonparametric portion of the model to obtain asymptotic normality of the sum of squared residuals. The approach yields tests of specification, significance, smoothness and concavity and allows for heteroskedastic residuals.

Type
Articles
Information
Econometric Theory , Volume 8 , Issue 4 , December 1992 , pp. 435 - 451
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

1.Bierens, H.Consistent model specification tests. Journal of Econometrics 20 (1982): 105–134.CrossRefGoogle Scholar
2.Brooke, A., Kendrick, D. & Meeraus, A.. GAMS. Redwood City, CA: Scientific Press, 1988.Google Scholar
3.Chui, C. & Smith, P.. A Note on Landau's Problem for Bounded Intervals. American Mathematical Monthly (1975): 927–929.CrossRefGoogle Scholar
4.De Boor, C.How small can one make the derivative of an interpolating function. Journal of Approximation Theory 13 (1975): 105–116.CrossRefGoogle Scholar
5.Dudley, R.M. A course on empirical processes. In Lecture Notes in Mathematics, École d'Été de Probabilités de Saint-Flour XII-1982. New York: Springer-Verlag, 1984.CrossRefGoogle Scholar
6.Epstein, L. & Yatchew, A.J.. Nonparametric hypothesis testing procedures and applications to demand analysis. Journal of Econometrics 30 (1985): 149–169.CrossRefGoogle Scholar
7.Favard, J.Sur Interpolation. Journal Mathematique Pures 19 (1940): 281–306.Google Scholar
8.Gallant, A.R.Unbiased determination of production technologies. Journal of Econometrics 20 (1982): 285–323.CrossRefGoogle Scholar
9.Hall, P.Integrated square error properties of kernel estimators of regression functions. Annals of Statistics 12 (1984): 241–260.CrossRefGoogle Scholar
10.Jennrich, R.Asymptotic properties of nonlinear least squares estimators. Annals of Mathematical Statistics 40 (1969): 633–643.CrossRefGoogle Scholar
11.Konakov, V.D.On a global measure of deviation for an estimate of the regression line. Theory of Probability and Its Applications 22 (1977): 858–868.CrossRefGoogle Scholar
12.Landau, E.Einige Ungleichungen fur zweimal differentzierbare functionen. Proceedings of the London Mathematical Society 13 (1913): 43–49.Google Scholar
13.Lee, B.J.A Model Specification Test Against the Nonparametric Alternative. Department of Economics, University of Colorado, 1991.Google Scholar
14.Nadaraya, E.A.A limit distribution of the square error deviation of nonparametric estimators of the regression function. Z. Wahrscheimlichkeitstheorie verw. Gabiete 64 (1974): 37–48.CrossRefGoogle Scholar
15.Pollard, D.Convergence of Stochastic Processes. New York: Springer-Verlag, 1984.CrossRefGoogle Scholar
16.Powell, M.J.D.Approximation Theory and Methods. Cambridge: Cambridge University Press, 1981.CrossRefGoogle Scholar
17.Powell, J., Stock, J. & Stoker, T.. Semiparametric estimation of index coefficients. Econometrica 57 (1989): 1403–1430.CrossRefGoogle Scholar
18.Ranga Rao, R.Relations between weak and uniform convergence of measures with applications. Annals of Mathematical Statistics 33 (1962): 659–680.Google Scholar
19.Robertson, T., Wright, F.T. & Dykstra, R.L.. Order Restricted Statistical Inference. New York: Wiley, 1988.Google Scholar
20.Rosenblatt, M.A Quadratic Measure of Deviation of Two-Dimensional Density Estimates and a Test of Independence. Annals of Statistics 3 (1975): 1–14.CrossRefGoogle Scholar
21.Stoker, T. Tests of Derivative Constraints. Sloan School of Management Working Paper no. 1649–85, 1985.Google Scholar
22.Van de Geer, S.A new approach to least squares estimation with applications. Annals of Statistics 15 (1987): 587–602.Google Scholar
23.Varian, H.Nonparametric analysis of optimizing behaviour with measurement error. Journal of Econometrics 30: (1985).CrossRefGoogle Scholar
24.Wooldridge, J.M. A Test for Functional Form Against Nonparametric Alternatives. MIT Working Paper, 1989.Google Scholar
25.White, H.Consequences and detection of misspecified nonlinear regression models. Journal of the American Statistical Association 76 (1981): 419–433.CrossRefGoogle Scholar
26.Yatchew, A.J. Some tests of nonparametric regressions models. In Barnett, W., Berndt, E., and White, H. (eds.), Dynamic Econometric Modelling, Proceedings of the Third International Symposium in Economic Theory and Econometrics. New York: Cambridge University Press, 1988, pp. 121–135.Google Scholar