1. Math
  2. Statistics And Probability
  3. let y1 y2 yn denote a random sample from...

Question: let y1 y2 yn denote a random sample from...

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c. Based on solved example 5.4.2 in the textbook (extended) Let 11 Yo denote a random sample from a population with the fol- lowing distribution if os y s 0 fr (y) elsewhere Consider the following estimators of 6 01 Y (i.e. you calculate the sample mean but you multply it by 02 ymax (ie. you take the largest observation in the sample) You may take it as given that E(Y) and that the CDF of Y is given by 0 if y 0 (y) 1 if y 1 (i.e. no need to show either of these) Answer the following questions: Show that 01 is an unbiased estimators of 0. Show that 02 is biased and find the direction of its bias? How would you adjust 02 to obtain an unbiased estimator of 0? Is 02 asymptotically unbiased? Hint: In order to show that 02 is biased first show that the PDF of max is given by: 2n
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