Nonparametric optimal density estimation for censored circular data Article Swipe
Conanec, Nicolas
,
Lacour, Claire
,
Ngoc, Thanh Mai Pham
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2512.07380
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2512.07380
We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first establish a lower bound for the mean integrated squared error in the case of Sobolev densities, thereby identifying the minimax rate of convergence for this estimation problem. We then derive a matching upper bound for the same risk, showing that the proposed estimator attains the minimax rate when the underlying density belongs to a Sobolev class. Finally, we develop a data-driven version of the procedure that preserves this optimal rate, thus yielding an adaptive estimator. The practical performance of the method is demonstrated through simulation studies.
Related Topics
Concepts
Mathematics
Minimax
Estimator
Upper and lower bounds
Applied mathematics
Sobolev space
Rate of convergence
Nonparametric statistics
Probability density function
Mathematical optimization
Density estimation
Function (biology)
Minimax estimator
Adaptive estimator
Mean squared error
Random variable
Matching (statistics)
Statistics
Nonparametric regression
Convergence (economics)
Projection (relational algebra)
Optimal estimation
Variable (mathematics)
Estimation theory
Smoothness
Linear regression
Kernel density estimation
Consistent estimator
Metadata
- Type
- preprint
- Landing Page
- https://doi.org/10.48550/arxiv.2512.07380
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7111383987
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7111383987Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2512.07380Digital Object Identifier
- Title
-
Nonparametric optimal density estimation for censored circular dataWork title
- Type
-
preprintOpenAlex work type
- Publication year
-
2025Year of publication
- Publication date
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2025-12-08Full publication date if available
- Authors
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Conanec, Nicolas, Lacour, Claire, Ngoc, Thanh Mai PhamList of authors in order
- Landing page
-
https://doi.org/10.48550/arxiv.2512.07380Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://doi.org/10.48550/arxiv.2512.07380Direct OA link when available
- Concepts
-
Mathematics, Minimax, Estimator, Upper and lower bounds, Applied mathematics, Sobolev space, Rate of convergence, Nonparametric statistics, Probability density function, Mathematical optimization, Density estimation, Function (biology), Minimax estimator, Adaptive estimator, Mean squared error, Random variable, Matching (statistics), Statistics, Nonparametric regression, Convergence (economics), Projection (relational algebra), Optimal estimation, Variable (mathematics), Estimation theory, Smoothness, Linear regression, Kernel density estimation, Consistent estimatorTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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| abstract_inverted_index.regression | 29 |
| abstract_inverted_index.simulation | 120 |
| abstract_inverted_index.underlying | 85 |
| abstract_inverted_index.constructed | 26 |
| abstract_inverted_index.convergence | 58 |
| abstract_inverted_index.data-driven | 96 |
| abstract_inverted_index.identifying | 53 |
| abstract_inverted_index.performance | 113 |
| abstract_inverted_index.probability | 7 |
| abstract_inverted_index.demonstrated | 118 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile |