Quantile regression in functional linear semiparametric model |
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Authors: | Tang Qingguo Linglong Kong |
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Affiliation: | 1. School of Economics and Management, Nanjing University of Science and Technology, Nanjing, People's Republic of China;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada |
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Abstract: | This paper proposes nonparametric estimation methods for functional linear semiparametric quantile regression, where the conditional quantile of the scalar responses is modelled by both scalar and functional covariates and an additional unknown nonparametric function term. The slope function is estimated using the functional principal component basis and the nonparametric function is approximated by a piecewise polynomial function. The asymptotic distribution of the estimators of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. The asymptotic distribution of the estimator of the unknown nonparametric function is also established. Simulation studies are conducted to investigate the finite-sample performance of the proposed estimators. The proposed methodology is demonstrated by analysing a real data from ADHD-200 sample. |
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Keywords: | Functional linear semiparametric model quantile regression asymptotic distribution convergence rate ADHD |
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