Multivariate Bayesian function estimation

Comments On`bayesian Backfitting' Bayesian Function Estimation

I warmly congratulate the authors on this paper. I am sure they will succeed in broadening acceptance of the Bayesian paradigm in inference in regression, by providing this well-written and accessible treatment of the use of Markov chain Monte Carlo (MCMC) in tting the important class of (generalised) additive models. The paper promotes several ideas. It can be interesting and revealing to exam...

Bayesian Methods for Function Estimation

Variance Function Estimation in Multivariate Nonparametric Regression

Variance function estimation in multivariate nonparametric regression is considered and the minimax rate of convergence is established. Our work uses the approach that generalizes the one used in Munk et al (2005) for the constant variance case. As is the case when the number of dimensions d = 1, and very much contrary to the common practice, it is often not desirable to base the estimator of t...

Nonparametric adaptive time-dependent multivariate function estimation

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the L-risk in the proposed spatio-temporal model as the intensity goes to zero, when the underlying unknown response function is assumed to belong to a ball of appropriately construc...

Kernel estimation of multivariate cumulative distribution function

A smooth kernel estimator is proposed for multivariate cumulative distribution functions (cdf), extending the work of Yamato [H. Yamato, Uniform convergence of an estimator of a distribution function, Bull. Math. Statist. 15 (1973), pp. 69–78.] on univariate distribution function estimation. Under assumptions of strict stationarity and geometrically strong mixing, we establish that the proposed...