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On the Bahadur representation of sample quantiles in some stationary multivariate autoregressive processes

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  • Dutta, Kalyan
  • Sen, Pranab Kumar

Abstract

It is shown here that Bahadur's [Ann. Math. Statist. (1966) 37, 577-580] almost sure (a.s.) asymptotic representation of a sample quantile for independent and identically distributed random variables holds under certain regularity conditions for a general class of stationary multivariate autoregressive processes. This yields the asymptotic (multi-) normality of the standardized forms of quantiles in autoregressive processes. Other useful applications will be considered in a subsequent paper.

Suggested Citation

  • Dutta, Kalyan & Sen, Pranab Kumar, 1971. "On the Bahadur representation of sample quantiles in some stationary multivariate autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 1(2), pages 186-198, June.
    • Handle: RePEc:eee:jmvana:v:1:y:1971:i:2:p:186-198
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    Cited by:

    1. Dominicy, Yves & Hörmann, Siegfried & Ogata, Hiroaki & Veredas, David, 2013. "On sample marginal quantiles for stationary processes," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 28-36.
    2. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.
    3. Dembińska, Anna, 2014. "Asymptotic behavior of central order statistics from stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 348-372.

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