Related papers: M-type penalized splines with auxiliary scale esti…
M-type smoothing splines are a broad class of spline estimators that include the popular least-squares smoothing spline but also spline estimators that are less susceptible to outlying observations and model-misspecification. However,…
Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model…
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the…
In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the…
This paper gives a comprehensive treatment of the convergence rates of penalized spline estimators for simultaneously estimating several leading principal component functions, when the functional data is sparsely observed. The penalized…
Regression spline is a useful tool in nonparametric regression. However, finding the optimal knot locations is a known difficult problem. In this article, we introduce the Non-concave Penalized Regression Spline. This proposal method not…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
P-splines are penalized B-splines, in which finite order differences in coefficients are typically penalized with an $\ell_2$ norm. P-splines can be used for semiparametric regression and can include random effects to account for…
We present an estimation procedure for nonlinear mixed-effects models in which the population trajectory is represented by penalized splines and adapted to individuals via subject-specific transformation parameters. By exploiting the mixed…
This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding…
This paper addresses asymptotic properties of general penalized spline estimators with an arbitrary B-spline degree and an arbitrary order difference penalty. The estimator is approximated by a solution of a linear differential equation…
This report studies local asymptotics of P-splines with $p$th degree B-splines and a $m$th order difference penalty. Earlier work with $p$ and $m$ restricted is extended to the general case. Asymptotically, penalized splines are kernel…
It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…
Regression splines are largely used to investigate and predict data behavior, attracting the interest of mathematicians for their beautiful numerical properties, and of statisticians for their versatility with respect to the applications.…
To perform regression analysis in high dimensions, lasso or ridge estimation are a common choice. However, it has been shown that these methods are not robust to outliers. Therefore, alternatives as penalized M-estimation or the sparse…
This paper discusses asymptotic theory for penalized spline estimators in generalized additive models. The purpose of this paper is to establish the asymptotic bias and variance as well as the asymptotic normality of the penalized spline…
Penalized spline regression is a popular method for scatterplot smoothing, but there has long been a debate on how to construct confidence intervals for penalized spline fits. Due to the penalty, the fitted smooth curve is a biased estimate…
In this paper we introduce a new method for automatically selecting knots in spline regression. The approach consists in setting a large number of initial knots and fitting the spline regression through a penalized likelihood procedure…