Let X1 , , Xn be independent and identically distributed Cauchy random variables with unknown parameters (,
Question:
Let X1
, …, Xn be independent and identically distributed Cauchy random variables with unknown parameters (θ, τ). Let X̄ and s 2
X be the sample mean and sample variance respectively. By writing Xi = θ + τεi
, show that the joint distribution of the configuration statistic A with components Ai = (Xi − X̄)/sX is independent of the parameters and hence that A is ancillary. [This result applies equally to any locationscale family where the εi are i.i.d. with known distribution.]
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Tensor Methods In Statistics Monographs On Statistics And Applied Probability
ISBN: 9781315898018
1st Edition
Authors: Peter McCullagh
Question Posted: