Summary
This exposition consists of two parts. The first one of them is devoted to surveying recent developments in the asymptotic distribution theory of the multivariate Cramér-von Mises statistic. The second part is a preview of some developments in the asymptotic distribution theory of the Hoeffding-Blum-Kiefer-Rosenblatt independence criterion in that the there quoted 1980 joint results with Derek S. Cotterill of the Department of national Defence, Ottawa, have not yet appeared elsewhere.
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
Anderson, T.W., Darling, D.A. (1952). Asymptotic theory of certain “goodness of fit” criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193–212.
Blum, J.R., Kiefer, J., Rosenblatt, M. (1961). Distribution free tests of independence based on the sample distribution function. Annals of Mathematical Statistics, 32, 485–498.
Cotterill, D.S., Csörgö, M. (1979). On the limiting distribution of and critical values for the multivariate Craér-von Mises Statistic. Carleton Mathematical Lecture Note No. 24
Cotterill, D.S., Csörgö, M. (1980). On the limiting distribution of and critical values for the Hoeffding-Blum-Kiefer- Rosenblatt independence criterion. Manuscript in preparation.
Csörgö, S. (1976). On an asymptotic expansion for the von Mises ω2 statistic. Acta Scientiarum Mathematicarum (Szeged), 38, 45–67.
Csörgö, M. (1979). Strong approximations of the Hoeffding, Blum, Kiefer, Rosenblatt multivariate empirical process. Journal of Multivariate Analysis, 9, 84–100.
Csörgö, M., Révész, P. (1975). A new method to prove Strassen type laws of invariance principle II. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 31, 261–269.
Csörgö, S., Stachó, L. (1980). A step toward an asymptotic xpansion for the Cramer-von Mises statistic. In Colloquia Mathematioa Societatis Janos Bolyai, 21, B. Gyires, ed. Analytic Function Methods in Probability Theory, North- Holland Publishing Company, Amsterdam, Pages 53–65.
DeWet, T. (1979). Cramer-von Mises tests for independence. Manuscript.
Dugue, D. (1969). Characteristic functions of random variables connected with Brownian motion and of the von Mises multi-dimensional ω2n. In Multivariate Analysis, Vol. 2, P. R. Krishnaiah, ed. Academic Press, New York. Pages 289–301.
Durbin, J. (1970). Asymptotic distributions of some statistics based on the bivariate sample distribution function. In Nonparametric Techniques in Statistical Inference, M. L. Puri, ed. Cambridge University Press. Pages 435–451.
Götze, F. (1979). Asymptotic expansions for bivariate von Mises functionals. Preprints in Statistics 49, University of Cologne.
Goodman, V. (1976). Distribution estimates for functionals of the two-parameter Wiener process. Annals of Probability, 4, 977–982.
Hoeffding, W. (1949). A nonparametric test of independence. Annals of Mathematical Statistics, 19, 546–557.
Komlós, J., Major, P., Tusnády, G. (1975). An approximation of partial sums of independent R.V.’s and the sample D.F.I. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 32, 111–131.
Krivyakova, E.N., Martynov, G.V., Tyurin Yu. N. (1977). On the distribution of the ω2 statistic in the multidimensional case. Theory of Probability and its Applications, 22, 406–410.
Rosenblatt, M. (1952). Limit theorems associated with variants of the von Mises statistic. Annals of Mathematical Statistics, 23, 617–623.
Tusnády, G. (1977a). A study of statistical hypotheses (in Hungarian). Candidatus Disseration, Hungarian Academy of Sciences.
Tusnády, G. (1977b). Strong invariance principles. In Recent Developments in Statistics J.R. Barra et al., eds. North-Holland Publishing Company, Amsterdam. Pages 289 –300.
Tusnády, G. (1977). A remark on the approximation of the sample DF in the multidimensional case. Periodica Mathematica Hungarica, 8, 53–55.
Zincenko, N.M. (1975). On the probability of exit of the Wiener random field for some surface (in Russian with English summary). Teorija Verojatnostei i Matematiceskaja Statistika (Kiev), 13, 62–69.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 D. Reidel Publishing Company
About this chapter
Cite this chapter
Csörgő, M. (1981). On the Asymptotic Distribution of the Multivariate Cramer-Von Mises and Hoeffding-Blum-Kiefer-Rosenblatt Independence Criteria. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8552-0_12
Download citation
DOI: https://doi.org/10.1007/978-94-009-8552-0_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-8554-4
Online ISBN: 978-94-009-8552-0
eBook Packages: Springer Book Archive