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Dependent versions of a central limit theorem for the squared length of a sample mean

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  • Saikkonen, Pentti

Abstract

Portnoy (1988) has proved a central limit theorem for the squared length of a sample mean by assuming that the underlying random vectors are independent and identically distributed and that their dimension increases with the sample size. Extensions of this result to martingale differences, useful in time series hypothesis testing, are derived and applied to a test of serial correlation.

Suggested Citation

  • Saikkonen, Pentti, 1995. "Dependent versions of a central limit theorem for the squared length of a sample mean," Statistics & Probability Letters, Elsevier, vol. 22(3), pages 185-194, February.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:3:p:185-194
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    References listed on IDEAS

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    1. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(4), pages 489-500, December.
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