Testing for a Constant Mean Function using Functional Regression

Jin Seo Cho (), Meng Huang and Halbert White
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Meng Huang: Department of Economics, University of California, San Diego, U.S.A.

No 915, Discussion Paper Series from Institute of Economic Research, Korea University

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).

Keywords: Davies Test; Functional Data; Hypothesis Testing; Integrated Conditional Moment Test; Misspecification; Mixture Distributions; Nuissance Parameters; Wald Test (search for similar items in EconPapers)
JEL-codes: C11 C12 C80 (search for similar items in EconPapers)
Pages: 57 pages
Date: 2009
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:iek:wpaper:0915

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