Choosing the penalty in nonparametric regression: short and long-range dependence
Abstract
In this work, we study the one-dimensional regression problem under random design and Gaussian errors. Our framework is very general: we make no prior assumptions about the design (which may be nonstationary and exhibit short or long-range dependence), nor do we assume that the errors are homoscedastic. We examine in detail the cases where the error process exhibits short or long-range dependence. We adopt a least-squares penalized strategy using piecewise polynomials to estimate the regression function, following the framework of Baron, Birg{é} and Massart [1999]. We derive explicit penalties, up to calibration constants, to obtain adaptive estimators for which we establish risk bounds. Since these penalties depend on the dependence properties of the error process, which are unknown in practice, we propose several adaptations of the dimension jump calibration algorithm to make our procedures fully data-driven.
Related
- Choosing the Dictionary and Penalty for IV-LASSO
- Plug-in Optimization Method for Penalty Parameters in Nonparametric GMANOVA model
- The Lambert Penalty: Logarithmic Shrinkage for Sparse Regression
- Recursive moment updates for scalable Bayesian nonparametric regression
- Nonparametric Regression with Measurement Error in Banach Spaces
BibTeX
@misc{parte2026choosing,
title = {{Choosing the penalty in nonparametric regression: short and long-range dependence}},
author = {Emmanuel Caron Parte and Jérôme Dedecker and Bertrand Michel},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29231},
eprint = {2609.29231},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05757235v1},
}
RIS
TY - UNPB
TI - Choosing the penalty in nonparametric regression: short and long-range dependence
AU - Emmanuel Caron Parte
AU - Jérôme Dedecker
AU - Bertrand Michel
PY - 2026
DA - 2026/09/23
PB - HAL
DO - 10.48550/arxiv.2609.29231
UR - https://hal.science/hal-05757235v1
AB - In this work, we study the one-dimensional regression problem under random design and Gaussian errors. Our framework is very general: we make no prior assumptions about the design (which may be nonstationary and exhibit short or long-range dependence), nor do we assume that the errors are homoscedastic. We examine in detail the cases where the error process exhibits short or long-range dependence. We adopt a least-squares penalized strategy using piecewise polynomials to estimate the regression function, following the framework of Baron, Birg{é} and Massart [1999]. We derive explicit penalties, up to calibration constants, to obtain adaptive estimators for which we establish risk bounds. Since these penalties depend on the dependence properties of the error process, which are unknown in practice, we propose several adaptations of the dimension jump calibration algorithm to make our procedures fully data-driven.
ER -