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Abstract:
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In this article we apply Fisher's fiducial idea to conduct statistical inference for wavelet regression. We first develop a general methodology for handling model selection problems within the fiducial framework. With this new methodology we then propose fiducial based methods for performing wavelet curve estimation, as well as constructing both pointwise and curve-wise confidence intervals. It is shown that, under some mild regularity conditions, both the new fiducial based pointwise and curve-wise confidence intervals have asymptotically correct coverage. Furthermore, simulation results show that these new fiducial based methods, especially for constructing pointwise confidence intervals, also possess promising empirical properties. To the best of our knowledge, this is the first time that the fiducial idea has been applied to a nonparametric estimation problem.
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