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Inference for sparse and dense functional data with covariate adjustments

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  • Liebl, Dominik

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.

Suggested Citation

  • Liebl, Dominik, 2019. "Inference for sparse and dense functional data with covariate adjustments," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 315-335.
    • Handle: RePEc:eee:jmvana:v:170:y:2019:i:c:p:315-335
    DOI: 10.1016/j.jmva.2018.04.006
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    References listed on IDEAS

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    1. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
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    5. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
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    7. Germán Aneiros & Philippe Vieu, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 27-32, March.
    8. Oleksandr Gromenko & Piotr Kokoszka, 2012. "Testing the equality of mean functions of ionospheric critical frequency curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(5), pages 715-731, November.
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    Cited by:

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    3. Konrad Menzel, 2023. "Transfer Estimates for Causal Effects across Heterogeneous Sites," Papers 2305.01435, arXiv.org, revised May 2024.
    4. Justin Petrovich & Matthew Reimherr & Carrie Daymont, 2022. "Highly irregular functional generalized linear regression with electronic health records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 806-833, August.

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