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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. 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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    4. Greg McSwiggan & Adrian Baddeley & Gopalan Nair, 2017. "Kernel Density Estimation on a Linear Network," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 324-345, June.
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