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Teor. Veroyatnost. i Primenen., 1996, Volume 41, Issue 3, Pages 533–560 (Mi tvp3134)  

This article is cited in 7 scientific papers (total in 7 papers)

On the distribution of the ratio of sums of random variables

S. Yu. Novak

Siberian State Academy of Geodesy

Abstract: We study the distribution of the ratio $Z_n$ of sums of random variables. Berry–Esseen-type estimates of the rate of convergence in the central limit theorem for $Z_n$ are given. In addition, second-order asymptotic expansions for $\mathbb E Z_n$ and $\mathbb E Z^2_n$ are presented.
The results are applied to the problems of nonparametric regression curve estimation, nonparametric tail index estimation, and nonparametric estimation of a hazard function.

Keywords: Berry–Esseen-type estimates, regression, tail index, hazard function, mean square error.

DOI: https://doi.org/10.4213/tvp3134

Full text: PDF file (1107 kB)

English version:
Theory of Probability and its Applications, 1997, 41:3, 479–503

Bibliographic databases:

Received: 26.08.1993

Citation: S. Yu. Novak, “On the distribution of the ratio of sums of random variables”, Teor. Veroyatnost. i Primenen., 41:3 (1996), 533–560; Theory Probab. Appl., 41:3 (1997), 479–503

Citation in format AMSBIB
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\by S.~Yu.~Novak
\paper On the distribution of the ratio of sums of random variables
\jour Teor. Veroyatnost. i Primenen.
\yr 1996
\vol 41
\issue 3
\pages 533--560
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\zmath{https://zbmath.org/?q=an:0892.60033}
\transl
\jour Theory Probab. Appl.
\yr 1997
\vol 41
\issue 3
\pages 479--503
\crossref{https://doi.org/10.1137/S0040585X97975228}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Yu. Novak, “On self-normalized sums and Student's statistic”, Theory Probab. Appl., 49:2 (2005), 336–344  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Markovich N.M., “On-line estimation of the tail index for heavy-tailed distributions with application to WWW-traffic”, 2005 Next Generation Internet Networks, 2005, 388–395  crossref  isi  scopus
    3. Rudge J.F., “Mantle pseudo–isochrons revisited”, Earth and Planetary Science Letters, 249:3–4 (2006), 494–513  crossref  isi  scopus
    4. Novak S.Y., Beirlant J., “The magnitude of a market crash can be predicted”, Journal of Banking & Finance, 30:2 (2006), 453–462  crossref  isi  scopus
    5. S. Yu. Novak, “On the accuracy of inference on heavy-tailed distributions”, Theory Probab. Appl., 58:3 (2014), 509–518  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. Vasiliev V.A., “A Truncated Estimation Method with Guaranteed Accuracy”, Ann. Inst. Stat. Math., 66:1 (2014), 141–163  crossref  mathscinet  zmath  isi  scopus
    7. Politis D.N., Vasiliev V.A., Vorobeychikov S.E., “Truncated Estimation of Ratio Statistics With Application to Heavy Tail Distributions”, Math. Methods Stat., 27:3 (2018), 226–243  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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