Probability and Information Theory pp 187-200 | Cite as

# Applications of almost surely convergent constructions of weakly convergent processes

Conference paper

First Online:

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Anderson, T. W. and Darling, D. A., Asymptotic theory of “goodness of fit” criteria based on stochastic processes. Ann. Math. Statist. 23, 193–212, 1952.MathSciNetCrossRefzbMATHGoogle Scholar
- 2.Bickel, P. J., Some contributions to the theory of order statistics. Proc. Fifth Berkeley Symp. Prob. Statist. 1, 575–591, 1967.MathSciNetzbMATHGoogle Scholar
- 3.Bickel, P. J. and Hodges, J. L. Jr., The asymptotic theory of Galton’s test and a related simple estimate of location. Ann. Math. Statist. 38, 73–89, 1967.MathSciNetCrossRefzbMATHGoogle Scholar
- 4.Billingsley, P., Weak Convergence of Probability Measures, to be published by Wiley and Sons, 1968.Google Scholar
- 5.Birnbaum, Z. W. and Marshall, A. W., Some multivariate Chebyshev inequalities with extensions to continuous parameter processes. Ann. Math. Statist. 32, 687–703, 1961.MathSciNetCrossRefzbMATHGoogle Scholar
- 6.Chibisov, D. M., Some theorems on the limiting behavior of empirical distribution functions. Trudy Matem. Inst. in V. A. Steklova. 71, 104–112, 1964.Google Scholar
- 7.Chibisov, D. M., An investigation of the asymptotic power of tests of fit. Th. Prob. and Applic. (Translated by SIAM.) 10, 421–437, 1965.MathSciNetCrossRefGoogle Scholar
- 8.Chernoff, H., Gastwirth, J.L. and Johns, M. V., Asymptotic distribution of linear combinations of functions of order statistics with applications to estimation. Ann. Math. Statist. 38, 52–72, 1967.MathSciNetCrossRefzbMATHGoogle Scholar
- 9.Dudley, R. M., Weak convergence of probabilities on non-separable metric spaces and empirical measures on Euclidean spaces. Ill. J. Math., 10, 109–126, 1966.MathSciNetzbMATHGoogle Scholar
- 10.Dudley, R. M., Distances of probability measures and random variables. Ann. Math. Statist. 39, 1968. To appear.Google Scholar
- 11.Hewitt, E. and Stromberg, K., Real and Abstract Analyses. Springer-Verlag, New York. 1965.CrossRefzbMATHGoogle Scholar
- 12.Iglehart, D. L. and Taylor, H., Weak convergence of a sequence of quickest detection problems. To appear in Ann. Math. Statist. 39, 1968.Google Scholar
- 13.Lientz, B. P., Distributions of Renyi and Kac type statistics, power of corresponding tests based on Suzuki-type alternatives. Tech. Rpt. No. 51. Univ. of Washington, 1968.Google Scholar
- 14.Moore, D.S., An elementary proof of asymptotic normality of linear functions of order statistics. Ann. Math. Statist. 39, 263–265, 1968.MathSciNetCrossRefzbMATHGoogle Scholar
- 15.Prohorov, Yu. V., Convergence of random processes and limit theorems in probability theory. Th. Prob. and Applic. (translated by SIAM) 1, 157–214, 1956.MathSciNetCrossRefGoogle Scholar
- 16.Pyke, R., Spacings. J.R.S.S. Ser. B. 27, 395–449, 1965.MathSciNetzbMATHGoogle Scholar
- 17.Pyke, R. and Shorack, G. R., Weak convergence of a two-sample empirical process and a new approach to Chernoff-Savage theorem. Ann. Math. Statist. 39, 755–771, 1968.MathSciNetCrossRefzbMATHGoogle Scholar
- 18.Pyke, R. and Root, D. H., An application of stopping times to obtain weak convergence. Tech. Rpt. No. 16, Univ. of Washington. (1968).Google Scholar
- 19.Skorokhod, A. V., Limit theorems for stochastic processes. Th. Prob. and Applic. (translated by SIAM) 1, 261–290, 1956.MathSciNetCrossRefzbMATHGoogle Scholar
- 20.Stigler, S. M., Linear functions of order statistics. Ph. D. Dissertation Univ. of California at Berkeley, 1967.Google Scholar
- 21.Wichura, M., On the weak convergence of non-Borel probabilities on a metric space. Ph.D. Dissertation, Columbia University, 1968.Google Scholar
- 22.Wilk, M. B. and Gnanadesikan, R., Probability plotting methods for the analysis of data. Biometrika, 55, 1–17, 1968.Google Scholar

## Copyright information

© Springer-Verlag 1969