Electronic Communications in Probability, Vol. 8 (2003) Paper no. 7 , pages 63-76.

A Law of the Iterated Logarithm for the Sample Covariance Matrix

Steven J. Sepanski

Bibliography with links to MathSciNet (Math. Reviews) articles

  1. Araujo, A. and Gine, E. (1980) The Central Limit Theorem for Real and Banach Valued Random Variables. John Wiley and Sons. New York. Math Review 83e:60003
  2. Billingsley, P. (1966)  Convergence of types in k-space. Z. Wahrsch. Verw. Gebiete. 5. 175-179.   Math Review 33#6665
  3. Dudley, R.M. (1989) Real Analysis and Probability. Chapman and Hall. New York.  Math Review 91g:60001
  4.  Feller, W.(1968)  An Introduction to Probability Theory and its Applications, Volume 1. Third Edition. John Wiley and Sons. New York. Math Review 42 #5292
  5. Feller, W.(1968) An extension of the law of the iterated logarithm to variables without variance. J. Math.

    6. Mechan.  18, 343-355. Math Review 38 #1721
  6. Gine, E. and Mason, D.M. (1998) On the LIL for self-normalized sums of iid random

    7. variables.  J. Theor. Probab.  v. 11 no. 2, 351-370. Math. Review 99e:60082
  7. Griffin, P.S. and Kuelbs, J.D. (1989) Self normalized laws of the iterated logarithm.  Ann. Probab.  17,

    8. 1571-1601.Math. Review 92e:60062
  8. Hahn, M.G. and Klass, M.J. (1980) Matrix normalization of sums of random vectors in the domain of attraction of the multivariate normal. Ann. Probab. 8 (1980), no. 2, 262--280. Math. Review 81d:60030
  9. Kuelbs, J. and Ledoux M. (1987) Extreme values and the law of the iterated logarithm.  Prob. Theory

    10. and Rel. Fields.   74, 319-340. Math. Review 87m:60021
  10.  Meerschaert, M. (1988) Regular variation in $\R^k.$  Proc. Amer. Math. Soc.  102, 341-348. Math. Review 96d:60034
  11.  Meerschaert, Mark M.and  Scheffler, Hans-Peter (2001) Limit distributions for sums of

    12.    independent random vectors. Heavy tails in theory and practice. Wiley Series in Probability and Statistics:
       Probability and Statistics. John Wiley & Sons, Inc., New York, 2001. Math. Review 2002i:60047
  12. Pruitt, W.E. (1981) General one sided laws of the iterated logarithm. Ann. Probab.   9, 1-48.  Math. Review 82k:60066
  13. Sepanski, S.J. (1994).Asymptotics for multivariate $t$-statistic and Hotelling's $T\sp 2$-statistic under infinite second moments via bootstrapping. J. Multivariate Anal.

    14. 49, no. 1, 41--54. Math. Review 96d:62092
  14. Sepanski, Steven J. (1994) Necessary and sufficient conditions for the multivariate

    15. bootstrap of the mean. Statist. Probab. Lett. 19 , no. 3, 205--216.   Math. Review 95d:62067
  15.  Sepanski, Steven J. (2002) Extreme values and the multivariate compact law of the iterated

    16.   logarithm. J. Theoret. Probab. 14   no. 4, 989--1018.   Math. Review 2002j:60052
  16. Sepanski, S. (2001) A law of the iterated logarithm for multivariate trimmed sums. Preprint.
  17. Sepanski, Steven J. (1996) Asymptotics for multivariate $t$-statistic for random

    18. vectors in the generalized domain of attraction of the multivariate normal law. Statist. Probab. Lett. 30 , no. 2, 179--188. Math. Review 97k:60042