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This paper provides a novel empirical prior for Bayesian wavelet in the nonparametric regression model. The prior centres the wavelet coefficient at the individual sample observation, and we make a modification on the empirical prior by introducing a fractional power. The optimal rates of the posterior contraction and posterior mean estimator are established by the fractional likelihood method over Besov spaces. Comparison with some methods in the literature indicates that the modified empirical method is superior in terms of the mean squared error.

Optimal convergence rates of Bayesian wavelet estimation with a novel empirical prior in nonparametric regression model