Let X,..., XnCauchy(0) where the sample size is odd (to ensure uniqueness of the MLE) which...

 

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Let X,..., XnCauchy(0) where the sample size is odd (to ensure uniqueness of the MLE) which has pdf f(x; 0) = 1 1 1 + (x-0) TER 0 ER (a) Show that the order statistics X(1) X(2) when are two polynomials over R identical?) (b) Is the sample median = median X, sufficient for ? Prove or disprove. X(n) are minimally sufficient for 0. (Hint: Let X,..., XnCauchy(0) where the sample size is odd (to ensure uniqueness of the MLE) which has pdf f(x; 0) = 1 1 1 + (x-0) TER 0 ER (a) Show that the order statistics X(1) X(2) when are two polynomials over R identical?) (b) Is the sample median = median X, sufficient for ? Prove or disprove. X(n) are minimally sufficient for 0. (Hint:

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Solution a To show that the order statistics are minimally sufficient for the Cauchy distribution we ... View the full answer