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Simultaneous confidence region of an embedded one-dimensional curve in multi-dimensional space

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  • Yamazoe, Hiroya
  • Naito, Kanta

Abstract

This paper focuses on the simultaneous confidence region of a one-dimensional curve embedded in multi-dimensional space. Local linear regression is applied component-wise to each variable in multi-dimensional data, which yields an estimator of the one-dimensional curve. A simultaneous confidence region of the curve is proposed based on this estimator and theoretical results for the estimator and the region are developed under some reasonable assumptions. Practically efficient algorithms to determine the thickness of the region are also addressed. The effectiveness of the region is investigated through simulation studies and applications to artificial and real datasets, which reveal that the proposed simultaneous confidence region works well.

Suggested Citation

  • Yamazoe, Hiroya & Naito, Kanta, 2024. "Simultaneous confidence region of an embedded one-dimensional curve in multi-dimensional space," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002025
    DOI: 10.1016/j.csda.2023.107891
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    References listed on IDEAS

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    1. Liu, Yang & Ruppert, David, 2021. "Density estimation on a network," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Adrian Baddeley & Aruna Jammalamadaka & Gopalan Nair, 2014. "Multitype point process analysis of spines on the dendrite network of a neuron," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(5), pages 673-694, November.
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    4. Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
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