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Testing for a Constant Mean Function using Functional Regression

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  • Jin Seo Cho

    ()
    (Department of Economics, Korea University, Seoul, South Korea)

  • Meng Huang

    (Department of Economics, University of California, San Diego, U.S.A.)

  • Halbert White

    ()
    (Department of Economics, University of California, San Diego, U.S.A.)

Abstract

In this paper, we study functional regression and its properties in testing the hypothesis of a constant zero mean function or an unknown constant non-zero mean function. As we show, the associated Wald test statistics have standard chi-square limiting null distributions, standard non-central chi-square distributions for local alternatives converging to zero at root-n rate, and are consistent against global alternatives. These properties permit computationally convenient tests for hypotheses involving nuisance parameters. In particular, we develop new alternatives to tests for mixture distributions and for regression misspecification, both of which involve nuisance parameters identified only under the alternative. In Monte Carlo studies, we find that our tests have well behaved levels. We find that the new procedures may sacrifice only exploit the covariance structure of the Gaussian processes underlying our statistics. Further, functional regression tests can have power better than existing methods that do not exploit this covariance structure, like the specification testing procedures of Bierens (1982, 1990) or Stinchcombe and White (1998).

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Bibliographic Info

Paper provided by Institute of Economic Research, Korea University in its series Discussion Paper Series with number 0915.

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Length: 57 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:iek:wpaper:0915

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Related research

Keywords: Davies Test; Functional Data; Hypothesis Testing; Integrated Conditional Moment Test; Misspecification; Mixture Distributions; Nuissance Parameters; Wald Test;

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References

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  1. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  2. Stinchcombe, Maxwell B & White, Halbert, 1992. "Some Measurability Results for Extrema of Random Functions over Random Sets," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 495-514, July.
  3. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  4. Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, vol. 57(3), pages 675-83, May.
  5. Donald W.K. Andrews, 1999. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Cowles Foundation Discussion Papers 1229, Cowles Foundation for Research in Economics, Yale University.
  6. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September.
  7. White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-70, February.
  8. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
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