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A Bayesian approach is considered to estimate the number of basis functions and the smoothing parameter of the hybrid splines non-parametric regression procedure. The method used to obtain the estimate of the regression curve and its Bayesian confidence intervals is based on the reversible jump MCMC (Green 1995). Illustrations with simulated data are provided and show good performance of the proposed approach over the existing methods.
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Dias et al. (2002) studied this question.
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