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Chapter 9: Confidence Intervals Q. 9.5

Discussion in 'CS1' started by Varun Dixit, Mar 20, 2020.

  1. Varun Dixit

    Varun Dixit Made first post

    In question, we have been asked to calculate "large-sample approximate variance" (i.e. CRLB) for MLE of exponential distribution. But since MLE of exp distribution is a "Biased Estimator" as E(1/X-bar) = Lambda × n / n-1, how can CRLB be calculated for it ? Doesn't CRLB only apply for unbiased estimator ? The Unbiased Estimator would be (n-1/n) x (1/X-bar). The difference between estimates under both is too big to igonre, due to small sample size of 20 in question. (Biased estimate = 0.11494 and Unbiased estimate = 0.1092)
     
  2. John Lee

    John Lee ActEd Tutor Staff Member

    Fair point. Although for large samples it does approach the unbiased results - this won't be the case here.
    However, for a paper based exam we are limited.
    We'd actually use a parametric bootstrap to calculate this accurately.
     

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