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The estimation of the correlation coefficient of bivariate data under dependence: Convergence analysis


  • Masry, Elias


Let {Xi,Yi} be jointly distributed second-order random variables with correlation coefficient r. The estimation of r from the observations is a classical problem which has been examined under the assumption of an i.i.d. setting. In this paper we examine the statistical properties of the correlation coefficient estimate when the process {Xi,Yi} is dependent, constituting either a strongly mixing process or asymptotically uncorrelated. We establish convergence in probability (with rates) as well as asymptotic normality for the estimation error and present an explicit expression for the asymptotic variance.

Suggested Citation

  • Masry, Elias, 2011. "The estimation of the correlation coefficient of bivariate data under dependence: Convergence analysis," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1039-1045, August.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1039-1045

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    References listed on IDEAS

    1. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    2. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    3. Tran, Lanh Tat, 1990. "Kernel density estimation under dependence," Statistics & Probability Letters, Elsevier, vol. 10(3), pages 193-201, August.
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