We propose two test statistics for use in inverse regression problems "Y"="K""&thgr;"+"ϵ", where "K" is a given linear operator which cannot be continuously inverted. Thus, only noisy, indirect observations "Y" for the function "&thgr;" are available. Both test statistics have a counterpart in classical...

Warping is an approach to the reduction and analysis of phase variability in functional observations, by applying a smooth bijection to the function argument. We propose a natural representation of warping functions in terms of a new type of elementary functions named 'warping component...

Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non-linearity in the smooth function estimates. This motivates the study of lack-of-fit tests based on the restricted maximum likelihood ratio statistic which tests...