In this paper we give a brief survey of penalized spline smoothing. Penalized spline smoothing is a general non-parametric estimation technique which allows to fit smooth but else unspecified functions to empirical data. While penalized spline regressions are quite popular in natural sciences only few applications can be found in economics. We present an example demonstrating how this non-param...

Accurate estimation of an underlying function and its derivatives is one of the central problems in statistics. Parametric forms are often proposed based on the expert opinion or prior knowledge of the underlying function. However, these strict parametric assumptions may result in biased estimates when they are not completely accurate. Meanwhile, nonparametric smoothing methods, which do not im...

For a smoothing spline or general penalized spline model, the smoothing parameter can be estimated using residual maximum likelihood (REML) methods by expressing the spline in the form of a mixed model. The possibility of bimodality in the profile log-likelihood function for the smoothing parameter of these penalized spline mixed models is demonstrated. A canonical transformation into independe...

We describe and contrast several different bootstrapping procedures for penalized spline smoothers. The bootstrapping procedures considered are variations on existing methods, developed under two different probabilistic frameworks. Under the first framework, penalized spline regression is considered an estimation technique to find an unknown smooth function. The smooth function is represented i...

The penalized spline is a popular method for function estimation when the assumption of “smoothness” is valid. In this paper, methods for estimation and inference are proposed using penalized splines under the additional constraints of shape, such as monotonicity or convexity. The constrained penalized spline estimator is shown to have the same convergence rates as the corresponding unconstrain...

A number of criteria exist to select the penalty in penalized spline regression, but the selection of the number of spline basis functions has received much less attention in the literature. We propose to use a maximum likelihood-based criterion to select the number of basis functions in penalized spline regression. The criterion is easy to apply and we describe its theoretical and practical pr...

Penalized Spline Estimation in the Partially Linear Model by Ashley D. Holland Co-Chairs: Matias D. Cattaneo and Virginia R. Young Penalized spline estimators have received considerable attention in recent years because of their good finite-sample performance, especially when the dimension of the regressors is large. In this project, we employ penalized B-splines in the context of the partially...