Bayesian Analysis of Multivariate Smoothing Splines
نویسنده
چکیده
A general version of multivariate smoothing splines with correlated errors and correlated curves is proposed. A suitable symmetric smoothing parameter matrix is introduced, and practical priors are developed for the unknown covariance matrix of the errors and the smoothing parameter matrix. An efficient algorithm for computing the multivariate smoothing spline is derived, which leads to an efficient Markov chain Monte Carlo method for Bayesian computation. Key to the computation is a natural decomposition of the estimated curves into components intrinsic to the problem that extend the notion of principal components. These intrinsic principal curves are useful both for computation and for interpreting the data. Numerical simulations show multivariate smoothing splines outperform univariate smoothing splines. The method is illustrated with analysis of a multivariate macroeconomic time series data set.
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