Approximation of noisy data using multivariate splines and finite element methods

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differential operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.

ANALISIS REGRESI NONPARAMETRIK SPLINE MULTIVARIAT UNTUK PEMODELAN INDIKATOR KEMISKINAN DI INDONESIA

The aim of this study is to obtain statistics models which explain the relationship between variables that influence the poverty indicators in Indonesia using multivariate spline nonparametric regression method. Spline is a nonparametric regression estimation method that is automatically search for its estimation wherever the data pattern move and thus resulting in model which fitted the data. This study, uses data from survey of Social Economy National (Susenas) and survey of Employment National (Sakernas) of 2013 from the publication of the Central Bureau of Statistics (BPS). This study yields two models which are the best model from two used response variables. The criterion uses to select the best model is the minimum Generalized Cross Validation (GCV). The best spline model obtained is cubic spline model with five optimal knots.