In this paper we consider the estimation of the link function and the parameter vector of a single-index model under a purely Bayesian perspective by using P-splines and assuming errors distributed according to a scale mixture of Normals, which includes, among others, the Student-t distribution. We have made explicit all the details of the MCMC algorithm used to sample the parameters of interest according to the posterior distribution. The results of the suggested procedure has been tested and shown via simulation and application to real data.

References:

[1] Antoniadis, A., Gregoire, G. and McKeague, I.,W. (2004). Bayesian estimation in single-index models. Statistica Sinica, 14:1147 – 1164.

[2] Eilers, P. and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2):89–121.

[3] Lang, S. and Brezger, A. (2004). Bayesian P-splines. Journal of Computational and Graphical Statistics, 13:183–212.

[4] Yu, Y. and Ruppert, D. (2002). Penalized spline estimation for partially linear singleindex models. Journal of American Statistical Association, 97(460):1042-1054.

Keywords: Single-index model; Scale mixture of normals; Bayesian P-splines; MCMC

Biography: PhD, University of California, Berkeley

Professor of Statistics, University of São Paulo, Brazil

Main fields of interest: Time series analysis, with applications in Physical Sciences, Economy and Finance

Brazilian Statistical Association Award, 2006

Mahalanobis Award, 2009