Abstract
Given two possible models for the distribution of a sequence of random variables (Xn)n≥1 (for the first model, the Xn’s are i.i.d; for the second model the distribution of each Xn is slightly perturbed), it is suggested to estimate the variation and Hellinger distances between the two possible distributions of (Xn, Xn+1,…, Xn+m). The result is derived from some useful inequalities about variation and Hellinger distances on product spaces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. ABOU-JAOUDE “Sur un théorème de non-existence d’estimateurs convergeanten probabilité” Comptes-rendus Acad. Sc. (France), série A, t. 278, p. 1445–1448 (1974).
D.A. FREEDMAN “A remark on the diference between Sampling with and without replacement” J. Amer. Statist. Ass., Vol 72, p. 681, (1977).
J. GEFFROY “Distance en variation des lois-produits” Séminaire de Statistique mathématique, Université Pierre et Marie Curie, Paris (1974–1975), unpublished.
J. GEFFROY “Asymptotic separation of distributions and convergence, properties of tests and estimators” in “Asymptotic theory of statistical tests and estimation” Chakravarti édit., Academic Press 1980, p. 159–178 (1979).
A. HILLION “Quelques questions de distances de lois de probabilité” Pub. Inst. Stat. Univ. de Paris, vol. XXIII, fasc 3–4, p. 37–88, (1978).
A. HILLION “Etude, du point de vue de la séparation asymptotique, de certaines questions de distance de lois de probabilité sur des espaces-produits, d’estimation ponctuelle et par réglons de confiance” Thèse Université Pierre et Marie Curie, Paris (1980).
W. HOEFFDING, J. WOLFOWITZ “Distinguishability of sets of distributions” Ann. Math. Statist., vol. 29, p. 700–718 (1958).
K. MATUSITA “A distance, and related statistics in multivariate, analysis” in “Multivariate, analysis” P.R. Krishnaiah edit., Academic Press p. 187–200 (1966).
R. MOCHE “Décantation et séparation asympto tique uniformes tests et estimateurs convergents, dans le cas d’observations indépendantes, équldlstribuées ou non” Thèse (première partie) Université des Sciences et Techniques de Lille (1977).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag New York Inc.
About this paper
Cite this paper
Hillion, A. (1983). “On the Use of Some Variation Distance Inequalities to Estimate the Difference between Sample and Perturbed Sample”. In: Florens, J.P., Mouchart, M., Raoult, J.P., Simar, L., Smith, A.F.M. (eds) Specifying Statistical Models. Lecture Notes in Statistics, vol 16. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5503-1_10
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5503-1_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90809-0
Online ISBN: 978-1-4612-5503-1
eBook Packages: Springer Book Archive