Smoothing metrics for measures on groups

S. T. Rachev; J. E. Yukich

Annales de l'I.H.P. Probabilités et statistiques (1989)

  • Volume: 25, Issue: 4, page 429-441
  • ISSN: 0246-0203

How to cite

top

Rachev, S. T., and Yukich, J. E.. "Smoothing metrics for measures on groups." Annales de l'I.H.P. Probabilités et statistiques 25.4 (1989): 429-441. <http://eudml.org/doc/77358>.

@article{Rachev1989,
author = {Rachev, S. T., Yukich, J. E.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {weak convergence; Tauberian theorem; locally compact Abelian group; metric kernels; smoothing metric; empirical measure},
language = {eng},
number = {4},
pages = {429-441},
publisher = {Gauthier-Villars},
title = {Smoothing metrics for measures on groups},
url = {http://eudml.org/doc/77358},
volume = {25},
year = {1989},
}

TY - JOUR
AU - Rachev, S. T.
AU - Yukich, J. E.
TI - Smoothing metrics for measures on groups
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1989
PB - Gauthier-Villars
VL - 25
IS - 4
SP - 429
EP - 441
LA - eng
KW - weak convergence; Tauberian theorem; locally compact Abelian group; metric kernels; smoothing metric; empirical measure
UR - http://eudml.org/doc/77358
ER -

References

top
  1. [A1] K.S. Alexander, Probability Inequalities for Empirical Processes and a Law of the Iterated Logarithm, Ann. Prob., Vol. 12, 1984, pp. 1041-1067; Correction, Vol. 15, 1987, pp. 428-430. Zbl0549.60024MR757769
  2. [BF] C. Berg and G. Forst, Potential Theory on Locally Compact Abelian Groups, Springer-Verlag, 1975. Zbl0308.31001MR481057
  3. [DDF] A. D'Aristotile, P. Diaconis and D. Freedman, On Merging of Probabilities, Technical Report No. 301, 1988, Dept of Statistics, Stanford, California. Zbl0698.60005
  4. [Du1] R.M. Dudley, Convergence of Baire Measures, Studia Mathematica, Vol. XXVII, 1966, pp. 251-268. Zbl0147.31301MR200710
  5. [Du2] R.M. Dudley, Probabilities and Metrics, Aarhus Universitet Lecture Notes Series, No. 45, 1976. Zbl0355.60004MR488202
  6. [Du3] R.M. Dudley, Universal Donsker Classes and MetricEntropy, Ann. Prob., Vol. 15, 1987, pp. 1306-1326. Zbl0631.60004MR905333
  7. [DP] R.M. Dudley and W. Philipp, Invariance Principles for Sums of Banach Space Valued Random Elements and Empirical Processes, Z. Wahr. v. Geb., Vol. 62, 1983, pp. 509-552. Zbl0488.60044MR690575
  8. [Fe] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, 1971, second edition, Wiley and Sons. Zbl0219.60003MR270403
  9. [GZ1] E. Giné and J. Zinn, Some Limit Theorems for Empirical Processes, Ann. Prob., Vol. 12, 1984, pp. 929-989. Zbl0553.60037MR757767
  10. [GZ2] E. Giné and J. Zinn, Lecture on the Central Limit Theorem for Empirical Processes, Lecture Notes in Mathematics, No. 1221, 1985, Springer, pp. 50-113. Zbl0605.60026MR875007
  11. [HR] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol. I, 1979, Springer-Verlag. Zbl0416.43001MR551496
  12. [KM] J. Kerstan and K. Matthes, Gleichverteilungseigenschaften von Faltungen von Verteilungsgesetzen auf lokalkompakten abelschen Gruppen, I., Math. Nachr., Vol. 37, 1968, pp. 267-312. Zbl0214.43603MR242206
  13. [Ko] A.N. Kolmogorov, Some Recent Work in the Field of Limit Theorems in Probability Theory, Moscow Vestnik, Vol. 10, 1953, pp. 29-38. Zbl0052.36202
  14. [Ma] P. Massart, Rates of Convergence in the Central Limit Theorem for Empirical Processes, Lecture Notes Math., No. 1193, 1986, pp. 73-109. Zbl0615.60032MR855853
  15. [Po] D. Pollard, Convergence of Stochastic Processes, Springer-Verlag, 1984. Zbl0544.60045MR762984
  16. [Ra] S.T. Rachev, Minimal Metrics in a Space of Real-Valued Random Variables, Soviet Math. Dokl., Vol. 23/2, 1981, pp. 425-428. Zbl0473.60025
  17. [RI] S.T. Rachev, and Ts.G. Ignatov, Ideal Quadratic Metrics, Stability Problems of Stochastic Models, Seminar Proceedings, V.N.I.I.S.I., Moscow), pp. 119-128 (Russian); J. Soviet Math, Vol. 35, No. 2, 1986, pp. 2386-2394 (English). Zbl0596.60017MR859218
  18. [RY] S.T. Rachev and J.E. Yukich, Rates for the CLT via New Ideal Metrics, Ann. Prob., Vol. 17, 1989, pp. 775-788. Zbl0675.60018MR985389
  19. [Ru1] W. Rudin, Fourier Analysis on Groups, Interscience Publishers, 1962. Zbl0107.09603MR152834
  20. [Ru2] W. Rudin, Personal communication, August 1986. 
  21. [Se] V.V. Senatov, On Some Properties of Metrics on the Set of Distribution Functions, Math. U.S.S.R. Sbornik, Vol. 31, No. 3, 1977, pp. 379-387. Zbl0387.60023
  22. [Si] E. Siebert, Convergence and Convolutions of Probability Measures on a Topological Group, Ann. Prob., Vol. 4, 1976, pp. 433-443. Zbl0338.60012MR413217
  23. [St] V. Strassen, The Existence of Probability Measures with Given Marginals, Ann. Math. Statist., Vol. 36, 1965, pp. 423-439. Zbl0135.18701MR177430
  24. [Sz] D. Szasz, On a Metrization of the Vague Convergence, Stud. Sci. Math. Hungar., Vol. 9, 1974, pp. 219-222. Zbl0325.60008MR391209
  25. [Va] V.S. Varadarajan, Measures on Topological Spaces (in Russian), Mathematicheskii Sbornik, Vol. 55, (97), 1961, pp. 35-100. Zbl0152.04202MR148838
  26. [Yu1] J.E. Yukich, The Convolution Metric dg, Math. Proc. Camb. Phil. Soc., Vol. 98, 1985, pp. 533-540. Zbl0576.60006MR803612
  27. [Yu2] J.E. Yukich, Uniform Exponential Bounds for the Normalized Empirical Process, Studia Mathematica, Vol. 84, No. 2, 1986, pp. 71-78. Zbl0624.60047MR871846
  28. [Zo] V.M. Zolotarev, Probability Metrics, Theory Prob. Appl., Vol. 28, (2), 1986, pp. 278-302. Zbl0533.60025MR700210

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.