Kanta Naito is a Professor in GSIS, Tohoku University. His research interest include mathematical statistics and applied statistics. In particular, he works on estimation problems for various functions.
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Keywords: Local Linear Estimator, Simultaneous Confidence Region
Abstract: We discuss 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 its gradient vector. The proposed region is a thin region that contains the estimates of the one-dimensional curve; for example, in the case of three-dimensional data, it looks like a sausage-shaped region. 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.
Related Papers
Hiroya Yamazoe, Kanta Naito, Simultaneous confidence region of an embedded one-dimensional curve in multi-dimensional space, Computational Statistics & Data Analysis, Volume 192, 2024, 107891, ISSN 0167-9473,
https://doi.org/10.1016/j.csda.2023.107891
