Estimation for functional linear semiparametric model
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Estimation for functional linear semiparametric model Tang Qingguo1 · Bian Minjie1 Received: 29 March 2020 / Revised: 27 October 2020 / Accepted: 4 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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
1 Introduction With modern technology development, functional data are observed frequently in fields such as in econometrics, biology, chemometrics, geophysics, the medical sciences, meteorology and neurosciences. Functional data are made up of repeated measurements taken as curves, surfaces or other objects varying over a continuum, such as the time and space. As a natural extension of the multivariate data analysis, functional data analysis (FDA) provides valuable insights by taking into account the smoothness of
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00362020-01215-y) contains supplementary material, which is available to authorized users.
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Tang Qingguo [email protected] School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China
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T. Qingguo, B. Minjie
high-dimensional covariates and provides new approaches for solving inference problems. The effectively infinite dimensional character of FDA is a source of many of its differences from conventional multivariate analysis. There is rich body of literature on FDA, for example, the monographs by Ramsay and Silverman (2005) and Hsing and Eubank (2015) provide comprehensive introduction and discussion to the topic of FDA. Cardot et al. (2003), Cai and Hall (2006) and Hall and Horowitz (2007) applied functional principal component analysis (FPCA) studying functional linear model. Chen et al. (2011) considered the single-index functional regression model. Chen and Müller (2012) developed a conditional quantile analysis method under a generalized functional regression framework. Wang et al. (2017) propose a robust functional dimension reductio
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