Functional partially linear single-index model with beta distribution

In this work, for depicting the relationship between a bounded scalar response and predictors including both scalars and functions, we develop a functional partially linear single-index model based on beta distribution, which can capture the bounded feature of the response well and also provides more flexibility. Approximating the unknown functions based on B-spline simultaneously, the parametric estimates of the proposed model are obtained. Under some conditions, the asymptotic properties of the resulting estimators, including the consistency and asymptotic normality, are derived. In addition, the finite sample performance of our method is validated through some simulation studies. Meantime, real data from the Alzheimer’s disease neuroimaging initiative (ADNI) study is investigated, and the results show that our proposed model outperforms competitors.