LinearRegression2

9252012 p kolm 6 sampling distribution of ols

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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. ©...
View Full Document

This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

Ask a homework question - tutors are online