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4 results

  • Central Limit Theorem for Absolute Deviations from the Sample Mean and Applications

  • D. L. McLeish
  • Journal:
    Canadian Mathematical Bulletin / Volume 22 / Issue 4 / 01 December 1979
    Published online by Cambridge University Press:
    20 November 2018, pp. 391-396
    Print publication:
    01 December 1979
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  • The following type of argument is rendered almost believable by its frequent occurrence in elementary courses in statistics. Let ξi be a sequence of independent identically distributed random variables with means μ variances σ2.

  • A Central Limit Theorem with Conditioning on the Distant Past

  • D. L. McLeish
  • Journal:
    Canadian Mathematical Bulletin / Volume 18 / Issue 2 / June 1975
    Published online by Cambridge University Press:
    20 November 2018, pp. 245-247
    Print publication:
    June 1975
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  • Serfling (1968) has considered a central limit theorem in which assumptions are made concerning the expectation of variables conditioned on their distant predecessors. Dvoretsky (1972, theorem 5.3) has continued this investigation. Serfling showed that both martingales and φ-mixing sequences satisfied his conditions, and Dvoretsky extended this to Strong mixing sequences of random variables.