Generalized Cramér–von Mises minimum distance estimator

Jitka Hrabáková and Václav Kůs

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 23, 7471-7487

Abstract: This article investigates the consistency and efficiency of generalized Cramér–von Mises (GCM) minimum distance estimators in the context of statistical estimation, focusing particularly on the L1 norm and the expected L1 norm. It presents new inequality between Kolmogorov and generalized Cramér–von Mises distances, leading to the proof of consistency of Cramér–von Mises estimator with the convergence rate of n−1/3, and consistency of GCM of the order of n−p/2(p+q) in the (expected) L1 norm. Through theoretical analysis and computer simulations, the study explores practical application of these estimators across various distribution types, contributing to the understanding of minimum distance estimation in statistical analysis. The computer simulation also suggests further possible improvements of proven L1 convergence rate of GCM up to n−1/2.

Date: 2025
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DOI: 10.1080/03610926.2025.2476734

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