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Unformatted text preview: 4/8/2010 1 Properties of At the end of the last lecture note, we considered the properties of the estimator 1 (of the parameter or coefficient 1 ). We can also consider properties of the estimator (of ). It turns out they are similar, i.e. 1) is an unbiased estimator of 2) is a consistent estimator of 3) As n increases, the distribution of is well approximated by a normal distribution, i.e. where Var( ) is given by a slightly more complicated formula (eq 4.22 in the textbook) that again you will not need to remember. 4) As usual ( 29 ( 29 SE Var = ( 29 ( 29 ,Var N Summary To summarize, we have This implies that This will be very useful for hypothesis testing and forming confidence intervals. ( 29 ( 29 ( 29 ( 29 1 1 1 ,Var , Var N N ( 29 ( 29 ( 29 ( 29 1 1 1 0,1 and 0,1 N N SE SE -- 4/8/2010 2 Hypothesis Testing - I Given our results, we can do hypothesis tests just as before, i.e 1) State hypotheses (and select significance level), e.g. H : 1 = c vs. H A : 1 c where c is the value you are testing that 1 equals. 2) Compute t STAT 3) Compare t STAT to the appropriate critical value. Reject H if the absolute value of the t STAT is greater than the critical value....
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This note was uploaded on 06/17/2010 for the course ECON 103 taught by Professor Sandrablack during the Spring '07 term at UCLA.
- Spring '07