We construct bootstrap conndence intervals for smoothing spline and smoothing spline ANOVA estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from exponential families. Several variations of bootstrap conndence intervals are considered and compared. We nd that the commonly used bootstrap percentile intervals are inferior to the T intervals and to...

In the study of smoothing spline estimators, some convolution-kernellike properties of the Green’s function for an appropriate boundary value problem, depending on the design density, are needed. For the uniform density, the Green’s function can be computed more or less explicitly. Then, integral equation methods are brought to bear to establish the kernel-like properties of said Green’s functi...

In this paper we give a basic derivation of smoothing and interpolating splines and through this derivation we show that the basic spline construction can be done through elementary Hilbert space techniques. Smoothing splines are shown to naturally separate into a filtering problem on the raw data and an interpolating spline construction. Both the filtering algorithm and the interpolating splin...

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...

We construct bootstrap confidence intervals for smoothing spline and smoothing spline ANOVA estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from exponential families. Several variations of bootstrap confidence intervals are considered and compared. We find that the commonly used bootstrap percentile intervals are inferior to the T intervals an...

A spline-backfitted kernel smoothing method is proposed for partially linear additive model. Under assumptions of stationarity and geometric mixing, the proposed function and parameter estimators are oracally efficient and fast to compute. Such superior properties are achieved by applying to the data spline smoothing and kernel smoothing consecutively. Simulation experiments with both moderate ...

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regre...

Linear parametric regression models of fMRI time series have correlated residuals. One approach to address this problem is to condition the autocorrelation structure by temporal smoothing. Smoothing splines with the degree of smoothing selected by generalized cross-validation (GCV-spline) provide a method to find an optimal smoother for an fMRI time series. The purpose of this study was to dete...