9252012 p kolm 6 sampling distribution of ols

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Unformatted text preview: . © P. KOLM 6 Sampling Distribution of OLS Estimators Main questions: What are the expected values of the least squares estimators? o Are they unbiased? What are the variances of the least squares estimators? o Are they efficient? Do they follow a normal distribution? o How do we use this for statistical inference? VER. 9/25/2012. © P. KOLM 7 Classical Linear Regression Assumptions (Two-Variable Case) Classical linear regression assumptions: The population model is linear in the parameters y = b0 + b1x + u [SLR.1] We can randomly sample from the population model, i.e. obtain a random sample of size n , {(x i , yi ) : i = 1,2,..., n } [SLR.2] E (u | x ) = 0 and thus E (ui | x i ) = 0 [SLR.3] There is variation in the x i [SLR.4] VER. 9/25/2012. © P. KOLM 8 OLS is Unbiased Result: Under the classical linear regression assumptions the estimates of the ˆ ˆ regression coefficients are unbiased, that is E (b ) = b and E (b ) = b 0 0 1 1 This means that the sampling distribution of our estimator is centered around the true regression parameters Remark: Remember unbiasedness is a description of the estimator – in a given sample we may be “near” or “far” from the true parameter VER. 9/25/2012. ©...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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