用狄利克雷核对单纯形上的回归曲面进行局部线性平滑。

IF 1.2 3区数学 Q2 STATISTICS & PROBABILITY

Statistical Papers Pub Date : 2025-01-01 Epub Date: 2025-05-14 DOI:10.1007/s00362-025-01708-8

Christian Genest, Frédéric Ouimet

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引用次数: 0

摘要

介绍了单纯形上回归曲面的局部线性光滑器。该估计器解决了由局部自适应狄利克雷核加权的最小二乘回归问题，保证了良好的边界性质。推广了Chen的单变量结果，得到了偏差、方差、均方误差和平均积分平方误差的渐近结果（数理统计，54(2):312- 323,2002）。仿真研究表明，所提出的具有Dirichlet核的局部线性估计器优于其文献中唯一的直接竞争对手，即Bouzebda等人提出的具有Dirichlet核的Nadaraya-Watson估计器（AIMS Math 9(9): 261995 -26282, 2024）。

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Local linear smoothing for regression surfaces on the simplex using Dirichlet kernels.

This paper introduces a local linear smoother for regression surfaces on the simplex. The estimator solves a least-squares regression problem weighted by a locally adaptive Dirichlet kernel, ensuring good boundary properties. Asymptotic results for the bias, variance, mean squared error, and mean integrated squared error are derived, generalizing the univariate results of Chen (Ann Inst Stat Math, 54(2):312-323, 2002). A simulation study shows that the proposed local linear estimator with Dirichlet kernel outperforms its only direct competitor in the literature, the Nadaraya-Watson estimator with Dirichlet kernel due to Bouzebda et al. (AIMS Math 9(9):26195-26282, 2024).

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来源期刊

Statistical Papers 数学-统计学与概率论

CiteScore

2.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.