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An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative

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  • Joel Horowitz

    (University of Iowa)

Abstract

This paper describes a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n-1/2. Some existing tests have non-trivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n-1/2. There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.

Suggested Citation

  • Joel Horowitz, 2000. "An Adaptive, Rate-Optimal Test of a Parametric Model Against a Nonparametric Alternative," Econometric Society World Congress 2000 Contributed Papers 0166, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0166
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    Cited by:

    1. Emanuela Ciapanna & Marco Taboga, 2019. "Bayesian Analysis of Coefficient Instability in Dynamic Regressions," Econometrics, MDPI, vol. 7(3), pages 1-32, June.
    2. Juan Carlos Escanciano & Kyungchul Song, 2007. "Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects," PIER Working Paper Archive 07-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Yanqin Fan & Qi Li, 2002. "A Consistent Model Specification Test Based On The Kernel Sum Of Squares Of Residuals," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 337-352.
    4. Dette, Holger & Hetzler, Benjamin, 2004. "Specification tests indexed by bandwidths," Technical Reports 2004,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, University Library of Munich, Germany.
    6. E. Guerre & Pascal Lavergne, 2000. "Minimax Rates for Nonparametric Specification Testing in Regression Models," Econometric Society World Congress 2000 Contributed Papers 0644, Econometric Society.
    7. Horowitz, Joel L. & Spokoiny, Vladimir G., 2000. "An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models," Working Papers 00-04, University of Iowa, Department of Economics.
    8. Emmanuel Guerre & Pascal Lavergne, 2001. "Rate-optimal data-driven specification testing in regression models," Econometrics 0107001, University Library of Munich, Germany.
    9. Ignacio N. Lobato, 2000. "A Consistent Test for the Martingale Difference Assumption," Econometric Society World Congress 2000 Contributed Papers 0278, Econometric Society.

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