Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 13
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Bulinski, Alexander V. and Rakitko, Alexander S. 2016. Simulation and Analytical Approach to the Identification of Significant Factors. Communications in Statistics - Simulation and Computation, Vol. 45, Issue. 5, p. 1430.
    Mancino, M. E. and Pratelli, L. 2001. Some Results of Stable Convergence for Exchangeable Random Variables in Hilbert Spaces. Theory of Probability & Its Applications, Vol. 45, Issue. 2, p. 329.
    Fortini, S. Ladelli, L. and Regazzini, E. 1997. A Central Limit Problem for Partially ExchangeableRandom Variables. Theory of Probability & Its Applications, Vol. 41, Issue. 2, p. 224.
    Vaillancourt, Jean 1995. Asymptotics for multisample statistics. Canadian Journal of Statistics, Vol. 23, Issue. 2, p. 171.
    Hu, Tien-Chung and Weber, N. C. 1994. On the invariance principle for exchangeable random variables. Journal of the Italian Statistical Society, Vol. 3, Issue. 3, p. 429.
    Ivanoff, B.G and Weber, N.C. 1992. Weak convergence of row and column exchangeable arrays. Stochastics and Stochastic Reports, Vol. 40, Issue. 1-2, p. 1.
    Horowitz, Joseph 1990. A uniform law of large numbers and empirical central limit theorem for limits of finite populations. Statistics & Probability Letters, Vol. 10, Issue. 2, p. 159.
    1990. Correction. Technometrics, Vol. 32, Issue. 3, p. 367.
    Robinson, J. 1989. LIMIT THEOREMS FOR STANDARDIZED PARTIAL SUMS OF WEAKLY EXCHANGEABLE ARRAYS. Australian Journal of Statistics, Vol. 31, Issue. 1, p. 200.
    Stein, Michael 1987. Large Sample Properties of Simulations Using Latin Hypercube Sampling. Technometrics, Vol. 29, Issue. 2, p. 143.
    Aldous, David J. 1985. École d'Été de Probabilités de Saint-Flour XIII — 1983. Vol. 1117, Issue. , p. 1.
    Frank Patterson, Ronald and Lee Taylor, Robert 1985. Strong laws of large numbers for triangular arrays of exchangeable random variables. Stochastic Analysis and Applications, Vol. 3, Issue. 2, p. 171.
    Daffer, Peter Z. 1984. Central limit theorems for weighted sums of exchangeable random elements in banach spaces(1). Stochastic Analysis and Applications, Vol. 2, Issue. 3, p. 229.
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

A martingale approach to central limit theorems for exchangeable random variables

  • N. C. Weber (a1)
Abstract

In this paper it will be shown that by an appropriate choice of σ-fields, martingale methods can be used to obtain simple proofs of many of the central limit theorems known for triangular arrays of exchangeable random variables.

Copyright
COPYRIGHT: © Applied Probability Trust 1980 
References
Hide All
Blum, J. R., Chernoff, H., Rosenblatt, M. and Teicher, H. (1958) Central limit theorems for interchangeable processes. Canad. J. Math. 10, 222–229.
Chernoff, H. and Teicher, H. (1958) A central limit theorem for sums of interchangeable random variables. Ann. Math. Statist. 29, 118–130.
De Finetti, B. (1930) Funzione caratteristica di un fenomeno aleatorio. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 4, 86–133.
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.
Dvoretzky, A. (1972) Asymptotic normality for sums of dependent random variables. Proc. 6th Berkeley Symp. Math. Statist. Prob. 2, 513–535.
Eagleson, G. K. (1975) Martingale convergence to mixtures of infinitely divisible laws. Ann. Prob. 3, 557–562.
Eagleson, G. K. and Weber, N. C. (1978) Limit theorems for weakly exchangeable arrays. Math. Proc. Camb. Phil. Soc. 84, 123–130.
Scott, D. J. (1973) Central limit theorems for marring's and for processes with stationary increments using a Skorokhod representation approach. Adv. Appl. Prob. 5, 119–137.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 166 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×