Optimal convergence rates of Bayesian wavelet estimation with a novel empirical prior in nonparametric regression model. Issue 3 (4th May 2022)

• Record Type: Journal Article
• Authors: Yu, Yuncai; Liu, Ling; Wu, Peng; Liu, Xinsheng
• Is Part Of: Statistics. Volume 56:Issue 3(2022)
• Page Start: 565
• Page End: 577
• Publication Date: 2022-05-04
• Subjects: Bayesian wavelet -- Besov spaces -- modified empirical prior -- fractional likelihood -- optimal convergence rate; 62G07 -- 62G08 -- 62G10 -- 62C20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2022.2075363
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : 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.