On analogs of the Hellinger metric

1992 ◽  
Vol 59 (4) ◽  
pp. 921-925
Author(s):  
V. M. Zolotarev
Keyword(s):  
Hellinger Metric

Generalized Hellinger metric and Audenaert's in-betweenness

2020 ◽  
Vol 585 ◽  
pp. 191-198 ◽  
Author(s):  
Raluca Dumitru ◽  
Jose A. Franco
Keyword(s):  
Hellinger Metric

scholarly journals MAXIMAL UNIFORM CONVERGENCE RATES IN PARAMETRIC ESTIMATION PROBLEMS

2009 ◽  
Vol 26 (2) ◽  
pp. 469-500
Author(s):  
Walter Beckert ◽  
Daniel L. McFadden
Keyword(s):  
Uniform Convergence ◽  
Convergence Rates ◽  
Optimality Criterion ◽  
Parametric Estimation ◽  
Probability Measures ◽  
Distributed Data ◽  
Mild Conditions ◽  
Estimation Problems ◽  
Stochastically Bounded ◽  
Hellinger Metric

This paper considers parametric estimation problems with independent, identically nonregularly distributed data. It focuses on rate efficiency, in the sense of maximal possible convergence rates of stochastically bounded estimators, as an optimality criterion, largely unexplored in parametric estimation. Under mild conditions, the Hellinger metric, defined on the space of parametric probability measures, is shown to be an essentially universally applicable tool to determine maximal possible convergence rates. These rates are shown to be attainable in general classes of parametric estimation problems.

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