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1 results

  • Some comments concerning a curious singularity

  • Paul D. Feigin
  • Journal:
    Journal of Applied Probability / Volume 16 / Issue 2 / June 1979
    Published online by Cambridge University Press:
    14 July 2016, pp. 440-444
    Print publication:
    June 1979

  • Consider the maximum likelihood estimation of θ based on continuous observation of the process X, which satisfies dXt = θXtdt + dWt. Feigin (1976) showed that, when suitably normalized, the maximum likelihood estimate is asymptotically normally distributed when the true value of θ ≠ 0. The claim that this asymptotic normality also holds for θ = 0 is shown to be false. The parallel discrete-time model is mentioned and the ramifications of these singularities to martingale central limit theory is discussed.