Mixture of partially functional linear regression

Abstract

The paper introduces a new mixture of partially functional linear models to characterise the relationship between a scalar response and mixture predictors of functional and covariate vector. The mixing proportions are allowed to change with a covariate, enhancing the flexibility of the proposed model. Utilizing basis function expansion, we develop a modified backfitting EM algorithm to estimate the regression functions. Furthermore, based on Fisher’s method, a maximum form test statistics, combining the p-values of each component of mixtures, is proposed for depicting whether the mixing proportions actually depend on the covariate. The asymptotic properties of the resulting estimators are established under mild conditions. To assess the finite sample performance of the estimators, several simulation studies are conducted. Finally, we analyze the motivating datasets to illustrate the powerfulness of the proposed procedure.