Stability Problems for Stochastic Models pp 190-203 | Cite as
On F-processes and their applications
Conference paper
First Online:
Received:
Abstract
We consider the f-divergences of probability measures on filtered spaces and define the corresponding f-processes. We show how the f-processes can be used for the investigation of the properties of probability measures and statistical estimators.
Keywords
f-divergence Hellinger distance Matusita distance f-process Hellinger process Matusita process convergence in variation entire asymptotic separation (Cn)-consistencyPreview
Unable to display preview. Download preview PDF.
References
- 1.M. Akahira. Asymptotic theory for estimation of location in nonregular cases, i: order of convergence of consistent estimators. Rep. Stat. Appl. Res., JUSE 22 (1975), p.8–26.MathSciNetGoogle Scholar
- 2.M. Akahira. Asymptotic theory for estimation of location in nonregular cases, ii: bounds of asymptotic distributions of consistent estimators. Rep.Stat.Appl. Re., JUSE 22 (1975) 3, p.3–19.MathSciNetMATHGoogle Scholar
- 3.I. Csiszár. Information-type measures of divergence of probability distributions. MTA III. Osztály Közleményei 17 (1967), p.123–149, 267–291MATHGoogle Scholar
- 4.J. Jacod. Processus de Hellinger, absolute continuité, contiguité. Tech. Rep., Dep. de Math., Université de Rennes,Rennes 1984.Google Scholar
- 5.Ju.M.Kabanov. The strong convergence of random process. Abstracts of the ICM Warsawa 1982-Congress.Google Scholar
- 6.C.H. Kraft. Some conditions for consistency and uniform consistency of statistical procedures. University of California. Publications in Statistics (1955), 2, 135–141MathSciNetMATHGoogle Scholar
- 7.L.Le Ca. On the asymptotic normality of estimates. Proc. of the Symposium to Honour Jerzey Neyman. (Warsaw, 1974), Warsaw, wn. (1977) p.203–217.Google Scholar
- 8.F.Liese.An estimation of Hellinger Integrals of Point Processes.Friedrich Schiller-Universität.Jena. Forschungsergebnisse.Eingang 12.1.1983, Nr: N/83/1.Google Scholar
- 9.R. Liptser,F. Pukelsheim.A. Shiryayev.On necessary and sufficient conditions of contiguity and entire asymptotic separation of probability measures.Uspehi mat. nauk, 37 (1982), 6,p.97–124.MATHGoogle Scholar
- 10.R.Liptser, A.Shiryayev. On the problem of "predictable" criteria of contiguity. In: Probability and Math. Statistics 1982, Lecture Notes in math., 1021, 1983.Google Scholar
- 11.J. Memin, A. Shiryayev.Distance de Hellinger-Kakutani des lois correspondant à deux processus à accroissement indépendants: critères d'absolute continuité et de singularité. Tech. Rept., Dept de Mat., Université de Rennes, Rennes 1984.Google Scholar
- 12.E.Valkeila,L.Vostrikova. An integral representation for the Hellinger distance (to appear in Mathematica Scandinavica).Google Scholar
- 13.E.Valkeila, L.Vostrikova. On "predictable" criteria of (C n)-consistency of estimators (submitted to Probability Theory and their Application).Google Scholar
- 14.L. Vostrikova. On criteria for C n-consistency of estimators. Stochastics 11 (1984), p.265–290.MathSciNetCrossRefMATHGoogle Scholar
- 15.L. Vostrikova. On necessary and sufficient conditions for convergence of probability measures in variation. Stochastic Processes and their Applications, 18 (1984) 1, p.99–112.MathSciNetCrossRefMATHGoogle Scholar
Copyright information
© Springer-Verlag 1987