Exercise 3

# Exercise 3 - University of California Department of...

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University of California D. Steigerwald Department of Economics Economics 241B Exercise 3 1. Let (X 1 ,…,X n ) be an independent and identically distributed sample of exponential random variables with parameter 0 , so that x X e x f t 0 0 0 ) ; ( where 0 x< and 0 > 0. a. Write the log-likelihood and derive the MLE for 0 . b. Explain the concepts of a sufficient statistic and a minimal sufficient statistic. Define the minimal sufficient statistic for 0 . What is the relation between the minimal sufficient statistic and the MLE? 2. Consider the following model in which t X is of dimension k×1 and the data are independent across observations . t t t U X Y To derive an estimator of β one can make a variety of assumptions concerning t X and the error. The weakest assumption about exogenous regressors is to assume A1:   0 t jt U X E for each j=1,…,k . Often, we are willing to make the stronger exogeneity assumption

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## This note was uploaded on 12/26/2011 for the course ECON 241b taught by Professor Staff during the Fall '08 term at UCSB.

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Exercise 3 - University of California Department of...

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