A multigrid preconditioner for tensor product spline smoothing

Penalized spline smoothing is a well-established, nonparametric regression method that is efficient for one and two covariates. Its extension to more than two covariates is straightforward but suffers from exponentially increasing memory demands and computational complexity, which brings the method to its numerical limit. Penalized spline smoothing with multiple covariates requires solving a large-scale, regularized least-squares problem where the occurring matrices do not fit into storage of common computer systems. To overcome this restriction, we introduce a matrix-free implementation of the conjugate gradient method. We further present a matrix-free implementation of a simple diagonal as well as more advanced geometric multigrid preconditioner to significantly speed up convergence of the conjugate gradient method. All algorithms require a negligible amount of memory and therefore allow for penalized spline smoothing with multiple covariates. Moreover, for arbitrary but fixed covariate dimension, we show grid independent convergence of the multigrid preconditioner which is fundamental to achieve algorithmic scalability.

A Time-Varying Fiscal Reaction Function for Brazil

This paper evaluates the sustainability of public debt in Brazil using monthly data from January 2003 to June 2016, based on the estimation of fiscal reaction functions with time-varying coefficients. Three estimation methods are considered: Kalman filter, penalized spline smoothing and time-varying cointegration. Besides indicating that the reaction of the primary deficit to variations in the debt/GDP ratio declined over most of the analyzed period, all these methods lead to the conclusion that the Brazilian public debt, given the parameters then in force, reached an unsustainable trajectory in the last years of the sample.

Baseline correction for Raman spectra using penalized spline smoothing based on vector transformation

A penalized spline smoothing method based on vector transformation (VTPspline) method has been proposed for baseline correction of Raman spectra.

Hedonic Analysis of Housing Sales Prices with Semiparametric Methods

This study estimates a hedonic price function using a semiparametric regression based on Penalized Spline Smoothing, and compares the price prediction performance with conventional parametric models. The excellent results obtained show that the semiparametric models allow to obtain a significant improvement in the prediction of housing sales prices.

Comparative Analysis for Robust Penalized Spline Smoothing Methods

Smoothing noisy data is commonly encountered in engineering domain, and currently robust penalized regression spline models are perceived to be the most promising methods for coping with this issue, due to their flexibilities in capturing the nonlinear trends in the data and effectively alleviating the disturbance from the outliers. Against such a background, this paper conducts a thoroughly comparative analysis of two popular robust smoothing techniques, theM-type estimator andS-estimation for penalized regression splines, both of which are reelaborated starting from their origins, with their derivation process reformulated and the corresponding algorithms reorganized under a unified framework. Performances of these two estimators are thoroughly evaluated from the aspects of fitting accuracy, robustness, and execution time upon the MATLAB platform. Elaborately comparative experiments demonstrate that robust penalized spline smoothing methods possess the capability of resistance to the noise effect compared with the nonrobust penalized LS spline regression method. Furthermore, theM-estimator exerts stable performance only for the observations with moderate perturbation error, whereas theS-estimator behaves fairly well even for heavily contaminated observations, but consuming more execution time. These findings can be served as guidance to the selection of appropriate approach for smoothing the noisy data.