Nonparametric regression on Lie groups with measurement errors

Jeon, Jeong Min; Park, Byeong U.; Keilegom, Ingrid Van

doi:10.1214/22-aos2218

Cited by 7 publications

(8 citation statements)

References 69 publications

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“…Our deconvolution density estimator generalizes the density estimator on S 1 introduced in Efromovich (1997) and the one on S 2 introduced in Healy et al (1998). Our deconvolution regression estimator also generalizes the regression estimator on S 1 introduced in Jeon et al (2022). We establish several nonasymptotic properties of our estimators.…”

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confidence: 88%

“…The aforementioned works only investigated the rates of convergence of their estimators. Recently, Jeon et al (2022) studied deconvolution regression for a predictor taking values on a general compact and connected Lie group. To the best of our knowledge, Jeon et al (2022) is the unique work that considered regression analysis for a manifold-valued predictor in the presence of measurement error.…”

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confidence: 99%

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Density estimation and regression analysis on hyperspheres in the presence of measurement error

Jeon

Keilegom

2023

Scandinavian J Statistics

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This paper studies density estimation and regression analysis with data observed on a general unit hypersphere and contaminated by measurement errors. We establish novel density and regression estimators, and study their asymptotic properties such as the rates of convergence and asymptotic normality. We also provide two types of asymptotic confidence intervals for both density and regression functions. One type is based on the asymptotic normality of their estimators and the other type is based on the empirical likelihood technique. We present practical details on the implementation of our method as well as simulation studies and real data analysis.This article is protected by copyright. All rights reserved.

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confidence: 88%

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confidence: 99%

Density estimation and regression analysis on hyperspheres in the presence of measurement error

Jeon

Keilegom

2023

Scandinavian J Statistics

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“…Our deconvolution regression estimator on S d also generalizes the deconvolution regression estimator on S 1 introduced in [33]. We build up a theoretical foundation for those general estimators.…”

Section: Introductionmentioning

confidence: 98%

“…All the aforementioned works on deconvolution density estimation studied only the rates of convergence of their estimators. Recently, [33] studied density estimation and regression analysis with contaminated Lie-group-valued predictor. To the best of our knowledge, [33] is the unique work that considered regression analysis with contaminated manifold-valued variables.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, [33] studied density estimation and regression analysis with contaminated Lie-group-valued predictor. To the best of our knowledge, [33] is the unique work that considered regression analysis with contaminated manifold-valued variables. However, since S d for d = 2 and d ≥ 4 are not a Lie group, it is important to study such unexplored cases.…”

Section: Introductionmentioning

confidence: 99%

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Density estimation and regression analysis on S^d in the presence of measurement error

Jeon¹,

Keilegom²

2023

Preprint

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This paper studies density estimation and regression analysis with contaminated data observed on the unit hypersphere S d for d ∈ N. Our methodology and theory are based on harmonic analysis on general S d . We establish novel nonparametric density and regression estimators, and study their asymptotic properties including the rates of convergence and asymptotic distributions. We also provide asymptotic confidence intervals based on the asymptotic distributions of the estimators and on the empirical likelihood technique. We present practical details on implementation as well as the results of numerical studies.

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Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error

Jeon

Keilegom

2023

Journal of Multivariate Analysis

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Nonparametric regression on Lie groups with measurement errors

Cited by 7 publications

References 69 publications

Density estimation and regression analysis on hyperspheres in the presence of measurement error

Density estimation and regression analysis on hyperspheres in the presence of measurement error

Density estimation and regression analysis on S^d in the presence of measurement error

Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error

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