Inference for sparse and dense functional data with covariate adjustments

JOURNAL OF MULTIVARIATE ANALYSIS

卷:170

Article

Liebl, Dominik¹ 

[1] Univ Bonn, Stat Abt, Adenauerallee 24-26, D-53113 Bonn, Germany

关键词: Functional data analysis;    Local linear kernel estimation;    Asymptotic normality;    Multiple bandwidth selection;    Finite-sample correction;   

DOI  :  10.1016/j.jmva.2018.04.006

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free