Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series A, Pt. 3, pp. 287--308

BAYESIAN NONPARAMETRIC REGRESSION USING WAVELETS

By

JEAN-FRANCOIS ANGERS, Université de Montréal, Canada

and

MOHAN DELAMPADY, Indian Statistical Institute, Bangalore, India

SUMMARY. Multi-resolution analysis is used here to derive a wavelet smoother as an estimated regression function for a given set of noisy data. The hierarchical Bayesian approach is employed to model the regression function using a wavelet basis and to perform the subsequent estimations. The Bayesian model selection tool of Bayes factor is used to select the optimal resolution level of the multi-resolution analysis. Error bands are provided as an index of estimation error. The methodology is illustrated with two examples and a simulation study.

AMS (1991) subject classification. Primary 62G08; secondary 62A15, 62F15.

Key words and phrases. Function estimation, Hierarchical Bayes, Model choice.

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