This paper introduces a framework for functional partially linear single-index models, offering a versatile approach for analyzing complex data structures. Functional data analysis techniques are combined with partially linear single-index models to accommodate the inherent variability and nonlinearity present in functional data. The proposed framework allows for the incorporation of both functional and scalar covariates, enabling a comprehensive analysis of multidimensional datasets. We present the formulation of the model, detailing the integration of functional components and linear indices, and discuss computational algorithms for parameter estimation and inference. The effectiveness of the framework is demonstrated through simulation studies and applications to real-world datasets, highlighting its flexibility and utility in capturing intricate relationships and patterns within data.

Functional data analysis, partially linear single-index models, multidimensional data analysis

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