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Volumn 11, Issue 2, 1998, Pages 351-370

On the LIL for Self-Normalized Sums of IID Random Variables

Author keywords

Feller class; Law of the iterated logarithm; Self normalized sums; Student t statistic

Indexed keywords


EID: 0032336168     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022675620729     Document Type: Article
Times cited : (15)

References (15)
  • 3
    • 25344443136 scopus 로고
    • A probabilistic approach to the asymptotic distribution of sums of independent, identically distributed random variables
    • Csörgo, S., Haeusler, E., and Mason, D. M. (1988). A probabilistic approach to the asymptotic distribution of sums of independent, identically distributed random variables. Adv. Appl. Math. 9, 259-333.
    • (1988) Adv. Appl. Math. , vol.9 , pp. 259-333
    • Csörgo, S.1    Haeusler, E.2    Mason, D.M.3
  • 4
    • 0039523070 scopus 로고
    • A universal Chung-type law of the iterated logarithm
    • Einmahl, U., and Mason, D. M. (1994). A universal Chung-type law of the iterated logarithm. Ann. Prob. 22, 1803-1825.
    • (1994) Ann. Prob. , vol.22 , pp. 1803-1825
    • Einmahl, U.1    Mason, D.M.2
  • 5
    • 0038078178 scopus 로고
    • On regular variation and local limit theorems
    • Feller, W. (1967). On regular variation and local limit theorems. In Proc. Fifth Berkeley Symp., Vol. 2, Part 1, pp. 373-388.
    • (1967) Proc. Fifth Berkeley Symp. , vol.2 , Issue.1 PART , pp. 373-388
    • Feller, W.1
  • 6
    • 0039378037 scopus 로고    scopus 로고
    • When is the student t-statistic asymptotically standard normal?
    • Giné, E., Götze, F., and Mason, D. M. (1997). When is the student t-statistic asymptotically standard normal? Ann. Prob. 25, 1514-1531.
    • (1997) Ann. Prob. , vol.25 , pp. 1514-1531
    • Giné, E.1    Götze, F.2    Mason, D.M.3
  • 7
    • 0039925127 scopus 로고
    • Approximate local limit theorems for laws outside domains of attractions
    • Griffin, P. S., Jain, N., and Pruitt, W. (1984). Approximate local limit theorems for laws outside domains of attractions. Ann. Prob. 12, 45-63.
    • (1984) Ann. Prob. , vol.12 , pp. 45-63
    • Griffin, P.S.1    Jain, N.2    Pruitt, W.3
  • 8
    • 0000139327 scopus 로고
    • Self-normalized laws of the iterated logarithm
    • Griffin, P. S., and Kuelbs, J. (1989). Self-normalized laws of the iterated logarithm. Ann. Prob. 17, 1571-1601.
    • (1989) Ann. Prob. , vol.17 , pp. 1571-1601
    • Griffin, P.S.1    Kuelbs, J.2
  • 9
    • 0000867820 scopus 로고
    • Some extensions of the LIL via self-normalization
    • Griffin, P. S., and Kuelbs, J., 1991). Some extensions of the LIL via self-normalization. Ann. Prob. 19, 380-395.
    • (1991) Ann. Prob. , vol.19 , pp. 380-395
    • Griffin, P.S.1    Kuelbs, J.2
  • 10
    • 84974306811 scopus 로고
    • On the asymptotic normality of self-normalized sums
    • Griffin, P. S., and Mason, D. M. (1991). On the asymptotic normality of self-normalized sums. Proc. Cambridge Phil. Soc. 109, 597-610.
    • (1991) Proc. Cambridge Phil. Soc. , vol.109 , pp. 597-610
    • Griffin, P.S.1    Mason, D.M.2
  • 11
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13-30.
    • (1963) J. Amer. Statist. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 12
    • 0042342296 scopus 로고
    • Domains of partial attraction and tightness conditions
    • Jain, N., and Orey, S. (1980). Domains of partial attraction and tightness conditions. Ann. Prob. 8, 584-599.
    • (1980) Ann. Prob. , vol.8 , pp. 584-599
    • Jain, N.1    Orey, S.2
  • 13
    • 0042342292 scopus 로고
    • Relative stability, characteristic functions and stochastic compactness
    • Maller, R. A. (1979). Relative stability, characteristic functions and stochastic compactness. J. Austral. Math. Soc. (Series A) 28, 499-509.
    • (1979) J. Austral. Math. Soc. (Series A) , vol.28 , pp. 499-509
    • Maller, R.A.1
  • 14
    • 0042843205 scopus 로고
    • The class of limit laws for stochastically compact normed sums
    • Pruitt, W. (1983). The class of limit laws for stochastically compact normed sums. Ann. Prob. 11, 962-969.
    • (1983) Ann. Prob. , vol.11 , pp. 962-969
    • Pruitt, W.1
  • 15
    • 0001738414 scopus 로고
    • The contribution to the sum of the summand of maximum modulus
    • Pruitt, W. (1987). The contribution to the sum of the summand of maximum modulus. Ann. Prob. 15, 885-896.
    • (1987) Ann. Prob. , vol.15 , pp. 885-896
    • Pruitt, W.1


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