On mean derivative estimation of longitudinal and functional data: from sparse to dense

Hassan Sharghi Ghale-Joogh and S. Mohammad E. Hosseini-Nasab ()
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Hassan Sharghi Ghale-Joogh: Shahid Beheshti University
S. Mohammad E. Hosseini-Nasab: Shahid Beheshti University

Statistical Papers, 2021, vol. 62, issue 4, No 20, 2047-2066

Abstract: Abstract Derivative estimation of the mean of longitudinal and functional data is useful, because it provides a quantitative measure of changes in the mean function that can be used for modeling of the data. We propose a general method for estimation of the derivative of the mean function that allows us to make inference about both longitudinal and functional data regardless of the sparsity of data. The $$L^2$$ L 2 and uniform convergence rates of the local linear estimator for the true derivative of the mean function are derived. Then the optimal weighting scheme under the $$L^2$$ L 2 rate of convergence is obtained. The performance of the proposed method is evaluated by a simulation study, and additionally compared with another existing method. The method is used to analyse a real data set involving children weight growth failure.

Keywords: Functional/longitudinal data; Mean derivative function; Weighting schemes; $$L^2$$ L 2 convergence; Uniform convergence; 62G20; 62G05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01173-5

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