Estimating a structural distribution function by grouping
Bert van Es, Stamatis Kolios
TL;DR
This paper investigates methods for estimating the structural distribution function in rare event scenarios, confirming the consistency of grouped estimators and highlighting the inconsistency of the natural estimator.
Contribution
It introduces a grouping method for estimation, proves its consistency, and provides a mean squared error bound, advancing understanding of estimation in rare event contexts.
Findings
Grouping estimator is consistent for large samples.
Natural estimator is inconsistent.
A mean squared error bound for the grouping method is derived.
Abstract
By the method of Poissonization we confirm some existing results concerning consistent estimation of the structural distribution function in the situation of a large number of rare events. Inconsistency of the so called natural estimator is proved. The method of grouping in cells of equal size is investigated and its consistency derived. A bound on the mean squared error is derived.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Statistical Methods and Inference · Financial Risk and Volatility Modeling