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.

中文翻译：

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具有伪观测的稀疏M估计的有限样本性质

在存在伪观测的情况下，我们提供了常规正则化统计标准的有限样本属性。在无罚损失函数和惩罚的正则性条件的受限强凸假设下，我们在正则化M估计量上得出非渐近误差范围。然后，将这种带有伪观测的惩罚框架应用于一些常用的基于copula的模型的M估计。这些理论结果得到了实证研究的支持。