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Vector Space Measures and Applications I pp 255–269Cite as

Some exponential moments with applications to density estimation, the empirical distribution function, and lacunary series

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Bibliography

  1. Bickel, P. J. and Rosenblatt, M. (1973), On some global measures of the deviations of density function estimates, Annals of Statistics, Vol. 1, 1071–1095.

    Article  MathSciNet  MATH  Google Scholar 

  2. Billingsley, P. (1968), Convergence of probability measures, John Wiley & Sons, New York.

    MATH  Google Scholar 

  3. Chung, K. L. (1949), An estimate concerning the Kolmogorov limit distribution, Trans. Amer. Math. Soc., Vol. 67, 36–50.

    MathSciNet  MATH  Google Scholar 

  4. Dudley, R. M. (1968), Distances of probability measures and random variables, Annals of Mathematical Statistics, Vol. 39, 1563–1572.

    MathSciNet  MATH  Google Scholar 

  5. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis II, Springer-Verlag, Berlin-Heidelberg-New York, 1967.

    MATH  Google Scholar 

  6. Kiefer, J. (1961), On large deviations of the empiric distribution function of vector chance variables and a law of the iterated logarithm, Pacific J. of Math., Vol. 11, 649–660.

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Kuelbs, Some exponential moments of sums of independent random variables, Trans. Amer. Math. Soc. (to appear).

    Google Scholar 

  8. Kuelbs, J. (1976), Estimation of the multi-dimensional probability density function; Mathematics Research Center Technical Report #1646, University of Wisconsin, Madison.

    Google Scholar 

  9. Kuelbs, J. and Woyczynski, W., Lacunary series and exponential moments, submitted for publication.

    Google Scholar 

  10. Nadaraya, É. A. (1965), On non-parametric estimates of density functions and regression curves, Theory of Probability and Its Applications, Vol. 10, 186–190.

    Article  MATH  Google Scholar 

  11. Parzen, E. (1962), On estimation of a probability density and mode, Ann. Math. Statistics, Vol. 33, 1065–1076.

    Article  MathSciNet  MATH  Google Scholar 

  12. Révész, P. (1976), On multivariate empirical density functions, preprint.

    Google Scholar 

  13. Rosenblatt, M. (1971), Curve estimates, Annals of Mathematical Statistics, Vol. 42, 1815–1842.

    Article  MathSciNet  MATH  Google Scholar 

  14. W. Rudin, Fourier Analysis on Groups, Interscience Tracts in Pure and Appl. Math., no. 12, New York, 1962.

    Google Scholar 

  15. R. Salem and A. Zygmund, La loi du logarithme itéré pour les sériés trigonométriques lacunaires, Bull. Sci. Math. 74 (1950), 209–224.

    MathSciNet  MATH  Google Scholar 

  16. Schuster, E. F. (1969), Estimation of a probability density function and its derivatives, Annals of Mathematical Statistics, Vol. 40, 1187–1195.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, University of Wisconsin, 53706, Madison, WI

    J. Kuelbs

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  1. J. Kuelbs
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Richard M. Aron Seán Dineen

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© 1978 Springer-Verlag

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Kuelbs, J. (1978). Some exponential moments with applications to density estimation, the empirical distribution function, and lacunary series. In: Aron, R.M., Dineen, S. (eds) Vector Space Measures and Applications I. Lecture Notes in Mathematics, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066850

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  • DOI: https://doi.org/10.1007/BFb0066850

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08668-0

  • Online ISBN: 978-3-540-35906-7

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