More and more data are observed in form of curves. Numerous applications in finance,
neuroeconomics, demographics and also weather and climate analysis make it necessary to
extract common patterns and prompt joint modelling of individual curve variation. Focus
of such joint variation analysis has been on fluctuations around a mean curve, a statistical
task that can be solved via functional PCA. In a variety of questions concerning the above
applications one is more interested in the tail asking therefore for tail event curves (TEC)
studies. With increasing dimension of curves and complexity of the covariates though one
faces numerical problems and has to look into sparsity related issues.
Here the idea of FActorisable Sparse Tail Event Curves (FASTEC) via multivariate
asymmetric least squares regression (expectile regression) in a high-dimensional framework
is proposed. Expectile regression captures the tail moments globally and the smooth loss
function improves the convergence rate in the iterative estimation algorithm compared with
quantile regression. The necessary penalization is done via the nuclear norm. Finite sample
oracle properties of the estimator associated with asymmetric squared error loss and nuclear
norm regularizer are studied formally in this paper.
As an empirical illustration, the FASTEC technique is applied on fMRI data to see if
individualís risk perception can be recovered by brain activities. Results show that factor
loadings over different tail levels can be employed to predict individualís risk attitudes.
high-dimensionalM-estimator, nuclear norm regularizer, factorization, expectile
regression, fMRI, risk perception, multivariate functional data