Penalized nonparametric scalar-on-function regression via principal coordinates.

A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call , one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty.

Pointwise influence matrices for functional-response regression.

We extend the notion of an influence or hat matrix to regression with functional responses and scalar predictors. For responses depending linearly on a set of predictors, our definition is shown to reduce to the conventional influence matrix for linear models. The pointwise degrees of freedom, the trace of the pointwise influence matrix, are shown to have an adaptivity property that motivates a two-step bivariate smoother for modeling nonlinear dependence on a single predictor.

On sample size estimation and re-estimation adjusting for variability in confirmatory trials.

Sample size estimation (SSE) is an important issue in the planning of clinical studies. While larger studies are likely to have sufficient power, it may be unethical to expose more patients than necessary to answer a scientific question. Budget considerations may also cause one to limit the study to an adequate size to answer the question at hand.