Inference for sparse and dense functional data with covariate adjustments

Dominik Liebl

Journal of Multivariate Analysis, 2019, vol. 170, issue C, 315-335

Abstract: We consider inference for the mean and covariance functions of covariate adjusted functional data using Local Linear Kernel (LLK) estimators. By means of a double asymptotic, we differentiate between sparse and dense covariate adjusted functional data — depending on the relative order of m (the discretization points per function) and n (the number of functions). Our simulation results demonstrate that the existing asymptotic normality results can lead to severely misleading inferences in finite samples. We explain this phenomenon based on our theoretical results and propose finite-sample corrections which provide practically useful approximations for inference in sparse and dense data scenarios. The relevance of our theoretical results is showcased using a real-data application.

Keywords: Functional data analysis; Local linear kernel estimation; Asymptotic normality; Multiple bandwidth selection; Finite-sample correction (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:170:y:2019:i:c:p:315-335

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DOI: 10.1016/j.jmva.2018.04.006

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