Abstract Penalized spline smoothing is a well-established, nonparametric regression method that efficient for one and two covariates. Its extension to more than covariates straightforward but suffers from exponentially increasing memory demands computational complexity, which brings the its numerical limit. with multiple requires solving large-scale, regularized least-squares problem where occu...

A number of methods have been proposed to estimate the period of a variable star; e.g., a recent approach uses smoothing spline regression to fit tentative periodic functions (light curves) and selects the period minimizing a robust goodness-of-fit criterion. These methods assume that measurement errors vary independently over time. Empirical evidence, however, indicates substantial temporal de...

This paper investigates a computationally simple variant of boosting, L 2 Boost, which is constructed from a functional gradient descent algorithm with the L 2-loss function. As other boosting algorithms, L 2 Boost uses many times in an iterative fashion a pre-chosen tting method, called the learner. Based on the explicit expression of reetting of residuals of L 2 Boost, the case with (symmetri...

The (modified) Newton method is adapted to optimize generalized cross validation (GCV) and generalized maximum likelihood (GML) scores with multiple smoothing parameters. The main concerns in solving the optimization problem are the speed and the reliability of the algorithm, as well as the invariance of the algorithm under transformations under which the problem itself is invariant. The propos...

Spline smoothing provides a powerful tool for estimating nonparametric functions. Most of the past work is based on the assumption that the random errors are independent. Observations are often correlated in applications; e.g., time series data, spatial data and clustered data. It is well known that correlation greatly a ects the selection of smoothing parameters, which are critical to the perf...