Factorizable Sparse Tail Event Curves with Expectiles

Abstract

Data are observed more and more in form of curves, thus prompting a joint modelling to find out common patterns and also individual variations. With increasing dimension of both explanatory and response variables, penalization approach with nuclear norm can help to estimating the high dimensional coefficient matrix and provides insight into common factors. In addition, in a variety of applications one is more interested in the tail behaviors. Tail event curve study may be identified through tail probabilities or more general through functions based on conditional tail events to discover the extremes which do not follow the majority among curves. ????? We employ FActorisable Sparse Tail Event Curves (FASTEC) with expectiles to implement multivariate expectile regression in a high-dimensional framework. Expectiles capture the tail moments globally and the smooth loss function improves the convergence rate in the iterative estimation algorithm compared with quantile regression. Finite sample oracle properties of the estimator associated expectile loss and nuclear norm regularizer are studied formally. ????? As an empirical illustration, our model is applied on fMRI data to see if individual’s risk perception can be recovered by brain activities. Results show that main factors can reflect the common patterns of curves. Factor loadings over different tail levels can help to find out the most risk-seeking and averse behaviours. Taking tail risks into consideration, individual’s risk attitudes can be predicted more precisely, especially the extremes. JEL classification : C38, C55, C61, C91, D87 Keywords : high-dimensional M -estimators, nuclear norm regularizer, factor analysis, expectile regression, fMRI, risk perception, multivariate functional data ?