eISSN: 2791-173X editor@grpublishing.org
All Journals
Submit your article

Global Multidisciplinary Journal

Open Access Peer Review International
Open Access

A FRAMEWORK FOR FUNCTIONAL PARTIALLY LINEAR SINGLE-INDEX MODELS: FORMULATION AND ANALYSIS

DOI https://doi.org/10.55640/gmj-abc115
PDF
Hui Zhang 1 ,
4 School of Statistics, East China Normal University, Shanghai, PR China

Abstract

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.

Keywords

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

References

📄 T.T. Cai, P. Hall, Prediction in functional linear regression, Ann. Statist. 34 (2006) 2159–2179.
📄 H. Cardot, F. Ferraty, P. Sarda, Functional linear model, Statist. Probab. Lett. 345 (1999) 11–22.
📄 H. Cardot, F. Ferraty, P. Sarda, Spline estimators for the functional linear model, Statist. Sinica 13 (2003) 571–591.
📄 R.J. Carroll, J. Fan, I. Gijbels, W.P. Wand, Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997) 477–489.
📄 D. Chen, P. Hall, H.G. Müller, Single and multiple index functional regression models with nonparametric link, Ann. Statist. 39 (2011) 1720–1747.
📄 C. Crambes, A. Kneip, P. Sarda, Smoothing splines estimators for functional linear regression, Ann. Statist. 37 (2009) 35–72.
📄 P. Hall, J.L. Horowitz, Methodology and convergence rates for functional linear regression, Ann. Statist. 35 (2007) 70–91.
📄 W. Härdle, P. Hall, H. Ichimura, Optimal smoothing in single-index models, Ann. Statist. 21 (1993) 157–178.
📄 Y. Li, T. Hsing, On rates of convergence in functional linear regression, J. Multivariate Anal. 98 (2007) 1782–1804.
📄 Z. Lin, J. Cao, L. Wang, H. Wang, A Smooth and Locally Sparse Estimator for Functional Linear Regression via Functional SCAD Penalty, 2015. arXiv preprint arXiv:1510.08547.
📄 J.O. Ramsay, B.W. Silverman, Functional Data Analysis, Springer, New York, 2005.
📄 H. Shin, Partial functional linear regression, J. Statist. Plann. Inference 139 (2009) 3405–3418.

How to Cite

Hui Zhang. (2023). A FRAMEWORK FOR FUNCTIONAL PARTIALLY LINEAR SINGLE-INDEX MODELS: FORMULATION AND ANALYSIS. Global Multidisciplinary Journal, 2(04), 01-06. https://doi.org/10.55640/gmj-abc115

Most read articles by the same author(s)

1 2 3 4 5 6 7 8 9 10 > >> 

Similar Articles

1-10 of 106

You may also start an advanced similarity search for this article.