Sankhya: The Indian Journal of Statistics

2006, Volume 68, Pt. 4, 513--541

On Pointwise Optimality of Bayes Facctor Wavelet Regression Estimators

Natalia Bochkina, Imperial College, London, UK
Theofanis Sapatinas, University of Cyprus, Cyprus

SUMMARY. We investigate the theoretical performance of Bayes factor estimators at a single point in wavelet regression models with independent and identically distributed errors that are not necessarily normally distributed. We compare these estimators in terms of their frequentist pointwise optimality in Besov spaces for certain combinations of error and prior distributions.

AMS (2000) subject classification. Primary 62G08; secondary 62C10, 62C12, 62C20.

Key words and phrases. Bayesian inference, Besov spaces, nonparametric regression, optimality, pointwise risk, wavelets.

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