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Biometrika Advance Access originally published online on October 3, 2009
Biometrika 2009 96(4):847-860; doi:10.1093/biomet/asp050
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© 2009 Biometrika Trust

Article

Generalized fiducial inference for wavelet regression

Jan Hannig

Department of Statistics and Operations Research, The University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3260, U.S.A. jan.hannig{at}unc.edu

Thomas C. M. Lee

Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong tlee{at}sta.cuhk.edu.hk

Received for publication 1 January 2008. Revision received 1 April 2009.
  Abstract

We apply Fisher’s fiducial idea to wavelet regression, first developing a general methodology for handling model selection problems within the fiducial framework. We propose fiducial-based methods for wavelet curve estimation and the construction of pointwise confidence intervals. We show that these confidence intervals have asymptotically correct coverage. Simulations demonstrate that they possess promising empirical properties.

Key Words: Bayesian wavelet prior • Generalized fiducial inference • Pointwise confidence interval • Statistical model selection • Tree constraint • Wavelet regression


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