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Stochastic Analysis and Applications Volume 15, 1997 - Issue 5
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Original Articles

Chung type strong laws for arrays of random elements and bootstrapping

Abolghassem Bozorgnia Department of Statistics, Mashhad University, Mashhad, Iran
,
Ronald. F. Patterson Department of Mathematics and Computer Science, Georgia State University, Atlanta, Ga, 30303, U.S.A
&
Robert L. Taylor Department of Statistics, University of Georgia, Athens, Ga, 30602, U.S.A
Pages 651-669 | Published online: 03 Apr 2007

References

  • Adler , A. , Rosalsky , A. and Taylor , R.L. 1992 . Some strong laws of large numbers for sums of random elements . Bull. Inst. Math.,Academia Sinica , 20 : 335 – 357 .
  • Athreya , K.B. , Ghosh , M. , Low , L.Y. and Sen , P.K. 1984 . Laws of large numbers for bootstrapped U-statistics . J.Statist.Planning and Inf , 9 : 185 – 194 .
  • Beck , A. 1963 . “ On the strong law of large numbers ” . In Ergodic Theory , 21 – 53 . New York : Academic Press .
  • Bickel , P.J. and Freedman , D.A. 1981 . Some asymptotic theory for the bootstrap . Annals of Statist , 9 : 1196 – 1217 .
  • Bozorgnia , A. , Patterson , R.F. and Taylor , R.L. 1993 . On strong laws of large numbers for arrays of rowwise independent random elements . Internat.J. Math. & Math. Sci , 16 : 587 – 592 .
  • Chung , K.L. 1947 . Note on some strong laws of large numbers . Amer.J.Math , 69 : 189 – 192 .
  • Hoffmann-Jorgensen , J. and Piser , G. 1976 . The law of large numbers and the central limit theorem in Banach spaces . Annals of Probability , 4 : 587 – 599 .
  • Hu , T.C. and Taylor , R.L. 1995 . On the strong law for arrays and for the bootstrap mean and variance , University of Georgia . Statistics Technical Report
  • Marcinkiewicz , J. and Zygmund , A. 1937 . Sur les fonctions independantes . Fund.Math , 29 : 60 – 90 .
  • Mourier , E. 1953 . Elements aleatories dan un espace de Banach . Ann.Inst Henri Poincare , 13 : 159 – 244 .
  • Stein , E. 1970 . Singular Integrals and Differentiability Properties of Functions , Princeton, N.J : Princeton Univ. Press .
  • Taylor , R.L. 1978 . “ Stochastic Convergence of Weighted Sums of Random Elements in Linear Spaces ” . In Lecture Notes in Mathematics , Vol. V672 , Springer-Verlag .
  • Taylor , R.L. and Hu , T.C. 1987 . Strong laws of large numbers for arrays of rowwise independent random elements . Internat. J. Math. & Math. Sci , 4 : 805 – 814 .
  • Woyczynski , W.A. 1978 . “ Geometry and martingales in Banach spaces. Part II ” . In Advances in Probability , Vol. 4 , 267 – 517 . Dekker .
  • Woyczynski , W.A. 1980 . On Marcinkiewicz-Zygmund law of large numbers . Prob.and Math.Stat , 1 : 117 – 131 .

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