The finite sample properties of sparse M-estimators with pseudo-observations

Benjamin Poignard; Jean David Fermanian

doi:10.1007/s10463-021-00785-4

The finite sample properties of sparse M-estimators with pseudo-observations

Benjamin Poignard
, Jean David Fermanian

Research output: Contribution to journal › Article › peer-review

Abstract

We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted strong convexity assumption of the unpenalized loss function and regularity conditions on the penalty, we derive non-asymptotic error bounds on the regularized M-estimator. This penalized framework with pseudo-observations is then applied to the M-estimation of some usual copula-based models. These theoretical results are supported by an empirical study.

Original language	English
Journal	Annals of the Institute of Statistical Mathematics
Volume	74
Issue number	1
DOIs	https://doi.org/10.1007/s10463-021-00785-4
Publication status	Published - 1 Feb 2022
Externally published	Yes

Keywords

Copulas
Non-convex regularizer
Pseudo-observations
Statistical consistency

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10.1007/s10463-021-00785-4

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abstract = "We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted strong convexity assumption of the unpenalized loss function and regularity conditions on the penalty, we derive non-asymptotic error bounds on the regularized M-estimator. This penalized framework with pseudo-observations is then applied to the M-estimation of some usual copula-based models. These theoretical results are supported by an empirical study.",

keywords = "Copulas, Non-convex regularizer, Pseudo-observations, Statistical consistency",

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AU - Fermanian, Jean David

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N2 - We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted strong convexity assumption of the unpenalized loss function and regularity conditions on the penalty, we derive non-asymptotic error bounds on the regularized M-estimator. This penalized framework with pseudo-observations is then applied to the M-estimation of some usual copula-based models. These theoretical results are supported by an empirical study.

AB - We provide finite sample properties of general regularized statistical criteria in the presence of pseudo-observations. Under the restricted strong convexity assumption of the unpenalized loss function and regularity conditions on the penalty, we derive non-asymptotic error bounds on the regularized M-estimator. This penalized framework with pseudo-observations is then applied to the M-estimation of some usual copula-based models. These theoretical results are supported by an empirical study.

KW - Copulas

KW - Non-convex regularizer

KW - Pseudo-observations

KW - Statistical consistency

UR - https://www.scopus.com/pages/publications/85103906957

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DO - 10.1007/s10463-021-00785-4

M3 - Article

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VL - 74

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 1

ER -

The finite sample properties of sparse M-estimators with pseudo-observations

Abstract

Keywords

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