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

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YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2408.07209

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. Statist. Math., 54(2) (2002), pp. 312-323]. 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, Nezzal and Elhattab [AIMS Math., 9(9) (2024), pp. 26195-26282].

Related Topics

Mathematics

Simplex

Dirichlet Distribution

Statistics

Combinatorics

Mathematical Analysis

Concepts

Smoothing Mathematics Simplex Linear regression Dirichlet distribution Regression Statistics Econometrics Combinatorics Mathematical analysis Boundary value problem

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2408.07209
PDF: https://arxiv.org/pdf/2408.07209
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4402426544

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DOI: https://doi.org/10.48550/arxiv.2408.07209

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

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-08-13

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Authors: Christian Genest, Frédéric Ouimet

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Landing page: https://arxiv.org/abs/2408.07209

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PDF URL: https://arxiv.org/pdf/2408.07209

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OA URL: https://arxiv.org/pdf/2408.07209

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Concepts: Smoothing, Mathematics, Simplex, Linear regression, Dirichlet distribution, Regression, Statistics, Econometrics, Combinatorics, Mathematical analysis, Boundary value problem

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Related works (count): 10

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