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density 18 Drponentt paramete (1) Find the method of moment estimator ô of 0. Show that ô is unbiased and consistent, and calculate its MSE. (2) Prove that the MLE ð of 0 is X(1) (the 1st order statistic). (3) Calculate the bias and MSE of Õ and prove that ð is consistent. (4) Which estimator do you prefer, ôô or ? Provide a brief explanation of your answer.

density 18 Drponentt paramete (1) Find the method of moment estimator ô of 0. Show that ô is unbiased and consistent, and calculate its MSE. (2) Prove that the MLE ð of 0 is X(1) (the 1st order statistic). (3) Calculate the bias and MSE of Õ and prove that ð is consistent. (4) Which estimator do you prefer, ôô or ? Provide a brief explanation of your answer.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider a random sample X1,..., X, from the distribution with density f(x; 0) = e-(a-0), r> 0 and parameter 0 > 0. Hint: you may find it useful to show that this density is in fact the density of a random variable Y + 0, where Y is Exponential with parameter 1. (1) Find the method of moment estimator ô of 0. Show that ô is unbiased and consistent, and calculate its MSE. (2) Prove that the MLE Õ of 0 is X(1) (the 1st order statistic). (3) Calculate the bias and MSE of ő and prove that ô is consistent. (4) Which estimator do you prefer, ô or ô? Provide a brief explanation of your answer.
Transcribed Image Text:Consider a random sample X1,..., X, from the distribution with density f(x; 0) = e-(a-0), r> 0 and parameter 0 > 0. Hint: you may find it useful to show that this density is in fact the density of a random variable Y + 0, where Y is Exponential with parameter 1. (1) Find the method of moment estimator ô of 0. Show that ô is unbiased and consistent, and calculate its MSE. (2) Prove that the MLE Õ of 0 is X(1) (the 1st order statistic). (3) Calculate the bias and MSE of ő and prove that ô is consistent. (4) Which estimator do you prefer, ô or ô? Provide a brief explanation of your answer.
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