Testing for a Constant Mean Function using Functional Regression
AbstractIn 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 InfoPaper provided by Institute of Economic Research, Korea University in its series Discussion Paper Series with number 0915.
Length: 57 pages
Date of creation: 2009
Date of revision:
Davies Test; Functional Data; Hypothesis Testing; Integrated Conditional Moment Test; Misspecification; Mixture Distributions; Nuissance Parameters; Wald Test;
Find related papers by JEL classification:
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
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