Penalized splines have gained much popularity as a flexible tool for smoothing and semi-parametric models. Two approaches have been advocated: 1) use a B-spline basis, equally-spaced knots and difference penalties (Eilers and Marx, 1996) and 2) use truncated power functions, knots based on quantiles of the independent variable and a ridge penalty (Ruppert, Wand and Carroll, 2003). We compare th...

Given a set of scattered data with derivative values. If the data is noisy or there is an extremely large number of data, we use an extension of the penalized least squares method of von Golitschek and Schumaker [Serdica, 18 (2002), pp.1001-1020] to fit the data. We show that the extension of the penalized least squares method produces a unique spline to fit the data. Also we give the error bou...

Penalized spline smoothing is a popular and flexible method of obtaining estimates in nonparametric regression but the classical least-squares criterion highly susceptible to model deviations atypical observations. estimation with resistant loss function natural remedy, yet this day asymptotic properties M-type penalized estimators have not been studied. We show paper that achieve same rates co...

We consider multidimensional penalized spline mixed models. Currie et al. (2006) emphasized the array nature of the method and Eilers et al. (2006) used multidimensional P -splines together with a new fast and compact algorithm. We combine these ideas and show how to represent multidiensional Psplines as mixed models and propose an atractive unified approach to models which include smooth and r...

We propose the randomized Generalized Approximate Cross Validation (ranGACV) method for choosing multiple smoothing parameters in penalized likelihood estimates for Bernoulli data. The method is intended for application with penalized likelihood smoothing spline ANOVA models. In addition we propose a class of approximate numerical methods for solving the penalized likelihood variational problem...

In this article, we study the estimations of partially linear single-index models (PLSiM) with repeatedmeasurements. Specifically, we approximate the nonparametric function by the polynomial spline, and then employ the quadratic inference function (QIF) together with profile principle to derive the QIF-based estimators for the linear coefficients. The asymptotic normality of the resulting linea...

This paper deals with a linear model of regression on quantiles when the explanatory variable takes values in some functional space and the response is scalar. We propose a spline estimator of the functional coefficient that minimizes a penalized L type criterion. Then, we study the asymptotic behavior of this estimator. The penalization is of primary importance to get existence and convergence.

Quantile regression predicts the τ -quantile of the conditional distribution of a response variable given the explanatory variable for τ ∈ (0, 1). The aim of this paper is to establish the asymptotic distribution of the quantile estimator obtained by penalized spline method. A simulation and an exploration of real data are performed to validate our results.