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1 results

  • Estimation of the mean of a stationary time series by sampling

  • David R. Brillinger
  • Journal:
    Journal of Applied Probability / Volume 10 / Issue 2 / June 1973
    Published online by Cambridge University Press:
    14 July 2016, pp. 419-431
    Print publication:
    June 1973

  • Let X(t), – ∞ < t < ∞, be a stationary time series with mean cx. Let 0 < τ1 < τ2 < … < τN ≦ T denote A given sampling times in the interval (0, T]. We determine the asymptotic distribution of the estimate [X(τ1) + … + X(τN)]/N of cx when the sampling times are fixed, satisfying a form of generalised harmonic analysis requirement, and when the sampling times are the times of events of a stationary point process independent of the series X(t). The results obtained may be viewed as non-standard central limit theorems.