BACKGROUND Smoothing methods are widely used to analyze epidemiologic data, particularly in the area of environmental health where non-linear relationships are not uncommon. This study focused on three different smoothing methods in Cox models: penalized splines, restricted cubic splines and fractional polynomials. OBJECTIVES The aim of this study was to assess the effects of prognostic facto...

The asymptotic properties of smoothing parameter estimates for smoothing splines are developed. We consider a variety of estimates including Generalized Cross Validation, Generalized Maximum Likelihood, and more generally Type II ML estimates and the properties of the marginal posterior mode. Under the usual Sobolov space frequentist assumptions on the function to be estimated , consistency and...

It has been shown that oral and nasal vowel pairs can differ substantially in their oro-pharyngeal configuration (besides the position of the velum), an effect that may lead to the enhancement of certain acoustic features associated with nasalization. We use real-time MRI to compare the lingual configuration of oral and nasal vowels in Brazilian Portuguese at various timepoints during the produ...

A new multivariate approximation scheme to scattered data on arbitrary bounded domains in Rd is developed. The approximant is selected from a space spanned (essentially) by corresponding translates of the ‘shifted’ thin-plate spline (‘essentially,’ since the space is augmented by certain functions in order to eliminate boundary effects). This scheme applies to noisy data as well as to noiseless...

[Her13] F.Hernoux, R.Béarée, L.Gajny, E.Nyiri, J.Bancalin, O.Gibaru, Leap Motion pour la capture de mouvement 3D par spline L1. Application à la robotique. GTMG 2013, Marseille, 27-28 mars 2013 [Gib1899] J. Willard Gibbs, lettre à l’éditeur, Nature 59 (April 27, 1899) 606. [Lav00] J.E. Lavery, Univariate Cubic Lp splines and shape-preserving multiscale interpolation by univariate cubic L1 splin...

Non parametric regression methods can be presented in two main clusters. The one of smoothing splines methods requiring positive kernels and the other one known as Nonparametric Kernel Regression allowing the use of non positive kernels such as the Epanechnikov kernel. We propose a generalization of the smoothing spline method to include kernels which are still symmetric but not positive semi d...

Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline smoother that is designed for covariance smoothing and can be used for sparse functional or longitudinal data. We propose a fast algorithm for covariance smoothing...