Estimation for functional linear semiparametric model

Tang Qingguo () and Bian Minjie
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Tang Qingguo: Nanjing University of Science and Technology
Bian Minjie: Nanjing University of Science and Technology

Statistical Papers, 2021, vol. 62, issue 6, No 12, 2799-2823

Abstract: Abstract We study a functional linear semiparametric model which is not only an extension of partially functional linear models, but also an extension of semiparametric models. We consider the case that a response is related to a functional predictor and several scalar variables and the functional predictor is observed at a set of discrete points with noise. We propose a new estimation procedure which combines functional principal component analysis and B-spline methods to estimate unknown parameters and functions in model. The asymptotic distribution of the estimators of slope parameters is derived and the global convergence rate of the estimator of unknown slope function is established. The convergence rate of the mean squared prediction error for a predictor is also established. Simulation studies are conducted to investigate the finite sample performance of the proposed estimators. A real data example based on real estate data is used to illustrate our proposed methodology.

Keywords: Functional linear semiparametric model; Functional principal component analysis; Asymptotic distribution; B-spline (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01215-y

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