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heteroskedasticity - Heteroskedasticity Heteroskedasticity...

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Heteroskedasticity Heteroskedasticity text: S text: S - W 4.9, 15.3~5, 16.3 W 4.9, 15.3~5, 16.3
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A. Consequence A. Consequence violating MLR/5: consequences: No effect on the unbiasedness of OLS estimators the appropriateness of R-squared/ adjusted R-square as goodness- of-fit measure Has effect on is biased the usual t-stat, F-stat invalid, even in large samples, with or without normality. OLS is no longer BLUE 2 1 var( | ,..., ) i k i u x x σ = m var( ) j β
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B. Remedy : B. Remedy : Heteroskedasticity Heteroskedasticity - robust Procedure robust Procedure MLR/1~4 hold; form of heteroskedasticity is unknown simple model OLS estimate A valid estimator of var ( β -hat ): 0 1 i i i y x u β β = + + l 1 1 2 ( ) ( ) i i i x x u x x β β = + l 2 2 1 2 2 ( ) var( ) ( ) i i i x x x x σ β = l 2 2 1 2 var( ) ( ) i x x σ σ β = l n l 2 2 1 2 2 ( ) var( ) ( ) i i i x x u x x β =
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how valid ?
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