#### Funded by the US National Science Foundation, grant DMS 1006281, June 2010 – May 2014

### Project Summary

The analysis of samples of curves (a.k.a. Functional Data Analysis) is a field of growing importance in Statistics. Samples of curves arise, for instance, in longitudinal studies where a random process is observed on groups of individuals. In most cases, the trajectories present systematic variability both in amplitude and location of the main features (for example, the pubertal spurt in growth curves). Functional regression models, which use certain input curves (e.g. neural activity) to explain other output curves (e.g. muscle activity) were mostly developed to deal with amplitude variability but not with time variability. The main goal of this project is to develop functional regression models that include time-warping components as an intrinsic part of the model, therefore allowing more efficient statistical inference.

### Publications

- Gervini, D. (2015). Dynamic Retrospective Regression for Functional Data.
*Technometrics***57**26-34.- Technical Supplement available.

- Gervini, D. (2015). Warped Functional Regression. Biometrika
**102**1-14.- Technical Supplement available.

- Gervini, D. (2014). Analysis of Aneurisk65 data: warped logistic discrimination.
*Electronic Journal of Statistics***8**1930-1936. - Gervini, D. and Carter, P.A. (2014). Warped Functional Analysis of Variance.
*Biometrics***70**526-535.- Technical Supplement available.

### Computer Programs

#### Warped functional ANOVA

The zip file WFAnova_Matlab contains the Matlab programs (and compiled MEX Fortran subroutines) used in Gervini and Carter (2014). See *Readme.txt* file in the package for a brief description of the programs. Depending on your platform and your Matlab installation, you may need to re-compile the Fortran subroutines; the Fortran source files are in WFAnova_Fortran.

#### Warped functional regression

The zip file WFRe_package contains the Matlab programs (and Fortran subroutines) used in Gervini (2015, *Biometrika*). Depending on your platform and your Matlab installation, you may need to re-compile the Fortran subroutines. The main programs in the package are:

*runWFRe*: estimates models sequentially; normally you are only going to use this program for estimation*WFRe*: main program; does most of the computations, but is typically invoked through runWFRe and not directly*pred_WFRe*: computes predictors of new response curves given new covariates*bootWFRe*: bootstrap estimators of the regression coefficients, useful for estimating standard deviations*cv5_WFRe*: computes five-fold cross-validation prediction errors

#### Dynamic retrospective functional regression

The zip file DRFR_package contains the Matlab programs used in Gervini (2015, *Technometrics*). The main programs are:

*drfr*: computes estimators, by building models sequentially*drfr_boot_res*: bootstrapped estimators (using residual resampling)*drfr_cv5*: five-fold cross-validation for model selection*pred_drfr*: computes predictors of response trajectories given explanatory trajectories

Last updated: 17 Apr 2016, 13:00 hs