Bulletin of the American Mathematical Society

An asymptotic representation of the sample distribution function

David R. Brillinger

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 75, Number 3 (1969), 545-547.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183530553

Mathematical Reviews number (MathSciNet)
MR0243659

Zentralblatt MATH identifier
0206.20602

Citation

Brillinger, David R. An asymptotic representation of the sample distribution function. Bull. Amer. Math. Soc. 75 (1969), no. 3, 545--547. https://projecteuclid.org/euclid.bams/1183530553


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References

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  • 2. P. Billingsley, Convergence of probability measures, Wiley, New York, 1968.
  • 3. K. L. Chung, An estimate concerning the Kolmogorov limit distribution, Trans. Amer. Math. Soc. 67 (1949), 36-50.
  • 4. K. Itô and H. P. McKean, Jr., Diffusion processes and their sample paths, Springer-Verlag, Berlin, 1965.
  • 5. J. Kiefer, The deviations in Skorokhod-Strassen approximation, Notices Amer. Math. Soc. 15 (1968), 936-937.
  • 6. R. Pyke and D. Root, An application of stopping times to obtain weak convergence, Technical Report No. 16, University of Washington, Seattle, Wash., 1968.
  • 7. W. A. Rosenkrantz, On rates of convergence for the invariance principle, Trans. Amer. Math. Soc. 129 (1967), 542-552.
  • 8. V. Strassen, Almost sure behavior of sums of independent random variables and martingales, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66), vol. II: Contributions to probability theory, Part 1, Univ. of California Press, Berkeley, Calif., 1967, pp. 315-343.