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How can we compare small sample statistical properties of two unbiased estimators of 00?

How can we compare small sample statistical properties of two unbiased estimators of 00?

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
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How can we compare small sample statistical properties of two unbiased estimators of 00? Why is the Gauss-Markov Theorem useful? What is the role of the asymmetric absolute loss function in quantile regression analysis? Why do we index the quantile regression coefficient 3, by 7 € (0, 1)? How does simultaneity in economic models lead to endogeneity in explanatory variables? How does the Method of Moments (MM) estimator differ from an OLS estimator in a linear regression model that satisfies the Gauss-Markov assumptions? What is the rationale of the Hausman test of regressor exogeneity? Under what as- sumptions is the test valid? Why does the Generalized Method of Moments (GMM) use the analogy principle? Why is Maximum Likelihood estimation in general more efficient than GMM? What is the reason for evaluating a ratio of two likelihoods in the Likelihood Ratio test?
Transcribed Image Text:How can we compare small sample statistical properties of two unbiased estimators of 00? Why is the Gauss-Markov Theorem useful? What is the role of the asymmetric absolute loss function in quantile regression analysis? Why do we index the quantile regression coefficient 3, by 7 € (0, 1)? How does simultaneity in economic models lead to endogeneity in explanatory variables? How does the Method of Moments (MM) estimator differ from an OLS estimator in a linear regression model that satisfies the Gauss-Markov assumptions? What is the rationale of the Hausman test of regressor exogeneity? Under what as- sumptions is the test valid? Why does the Generalized Method of Moments (GMM) use the analogy principle? Why is Maximum Likelihood estimation in general more efficient than GMM? What is the reason for evaluating a ratio of two likelihoods in the Likelihood Ratio test?
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Consider two estimators, θ^01 and θ^02. With the assumption that two estimators are unbiased, it is to be defined that:

E(θ^01)=θ0 and E(θ^02)=θ0.

The objective is to compare the estimators using the small sample (or finite sample) statistical properties.

 

 

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