Strong approximation for the deviation of kernel copula estimators
Diam Ba, Seck Cheikh Tidiane, Lo Gane Samb
TL;DR
This paper establishes a strong uniform law of the iterated logarithm for the maximal deviation of various kernel copula estimators, aiding in their consistency analysis.
Contribution
It provides the first uniform in bandwidth law of the iterated logarithm for kernel copula estimators, including local linear, mirror-reflection, and transformation methods.
Findings
Proves a uniform law of the iterated logarithm for kernel copula estimators.
Shows these results are useful for establishing strong uniform consistency.
Applies to local linear, mirror-reflection, and transformation estimators.
Abstract
We prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of kernel copula estimators from their expectations. We deal especially with the \textit{local linear}, the \textit{mirror-reflection} and the \textit{transformation} estimators. These results are useful for establishing the strong uniform in bandwidth consistency of these kernel estimators.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Statistical Methods and Inference · Stochastic processes and financial applications