Weakly approaching sequences of random distributions

Journal of Applied Probability

Volumn 37, Issue 3, 2000, Pages 807-822

  Belyaev, Yuri ^a   Sjöstedt De Luna, Sara ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

Bootstrap; Continuity theorem; L vy metric; Resampling; Uniform metric; Weak convergence; Weakly approaching sequences

Indexed keywords

EID: 85037755843     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200016016     Document Type: Article

References (21)

1. ATHREYA, K. B. (1987). Bootstrap, of the mean in the infinite variance case. Ann. Statist. 15, 724-731.
2. BELYAEV, Y. K. (1995). Bootstrap, Resampling and Mallows Metric. Lecture Notes 1, Dept Mathematical Statistics, Umeå University, Sweden.
3. BELYAEV, Y. K. AND NILSSON, L. (1997). Parametric maximum likelihood estimators and resampling. Res. Rept 1997-15, Dept Mathematical Statistics, Umeå University, Sweden.
4. BELYAEV, Y. K. AND SELEZNJEV, O. (2000). Approaching in distribution with applications to resampling of stochastic processes. Scand. J. Statist. 27, 371-384.
5. BELYAEV, Y. K. AND SJÖSTEDT, S. (1997). Resampling from independent heterogeneous random variables with varying mean values. Theory Stoch. Proc. 3, 121-131.
6. BICKEL, P. J. AND FREEDMAN, D. A. (1981). Some asymptotic theory for the bootstrap. Ann. Statist. 9, 1196-1217.
7. BILLINGSLEY, P. (1968). Convergence of Probability Measures. John Wiley, New York.
8. CRAMÉR, H. (1946). Mathematical Methods of Statistics. Princeton University Press.
9. DAVISON, A. C. AND HINKLEY, D. V. (1997). Bootstrap Methods and their Application. Cambridge University Press.
10. DUDLEY, R. M. (1989). Real Analysis and Probability. Chapman and Hall, New York.
11. EFRON, B. AND TIBSHIRANI, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.
12. KLEBANOV, L. B., RACHEV, S. T. AND SZEKELY, G. J. (1999). Pre-limit theorems and their applications. Acta Appl. Math. 58, 159-174.
13. NILSSON, L. AND BELYAEV, Y. K. (1998). Application of resampling to exponential and logistic regression. Res. Rept 1998-1, Dept Mathematical Statistics, Umeå University, Sweden.
14. PARTHASARATHY, K. R. (1977). Introduction to Probability and Measure. Macmillan, Delhi.
15. RACHEV, S. T. (1991). Probability Metrics and the Stability of Stochastic Models. John Wiley, Chichester.
16. SEARLY, S. R. (1987). Linear Models for Unbalanced Data. John Wiley, New York.
17. SHAO, J. AND TU, D. (1995). The Jackknife and Bootstrap. Springer, New York.
18. SHIRYAYEV, A. N. (1996). Probability, 2nd edn. Springer, New York.
19. SJÖSTEDT, S. (2000). Resampling m-dependent random variables with applications to forecasting. Scand. J. Statist. 27, 543-561.
20. VAN DER VAART, A. W. AND WELLNER, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York.
21. WU, C. F. J. (1986). Jackknife, bootstrap and other resampling methods in regression analysis. Ann. Statist. 14, 1261-1295.