Mathematics – Statistics Theory
Scientific paper
2009-09-07
Annals of Statistics 2009, Vol. 37, No. 6A, 3307-3329
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/09-AOS686 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/09-AOS686
Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the nature of the functional relationship, we aim to estimate the directional derivatives and gradients of the response with respect to the predictor functions. In statistical applications and data analysis, functional derivatives provide a quantitative measure of the often intricate relationship between changes in predictor trajectories and those in scalar responses. This approach provides a natural extension of classical gradient fields in vector space and provides directions of steepest descent. We suggest a kernel-based method for the nonparametric estimation of functional derivatives that utilizes the decomposition of the random predictor functions into their eigenfunctions. These eigenfunctions define a canonical set of directions into which the gradient field is expanded. The proposed method is shown to lead to asymptotically consistent estimates of functional derivatives and is illustrated in an application to growth curves.
Hall Peter
Müller Hans-Georg
Yao Fang
No associations
LandOfFree
Estimation of functional derivatives does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Estimation of functional derivatives, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Estimation of functional derivatives will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-295274