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.)
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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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Paper provided by Institute of Economic Research, Korea University in its series Discussion Paper Series with number
0915.
Find related papers by JEL classification: C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
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