# Econ7630_Exam1b

 Parameter Estimation Framework 1. Population Y2. E[Y] = @3. Var(Y) = sig24. Assume Y1, Y2, . . ., Yn is a random sample from population5. Assume Yi are independtly and identically distributed (iid)6. ^ indicates estimate Estimation of @ Method 1: Method of Moments 1. E[Yi] = @ "population moment"2. `Y = ^@ = sum1-n(Yi/n) "sample moment""sum..." is the Estimator, which is an expression Estimation of @ Method 2: Minimize 1. s = sum1-n(yi - @)2 given yi(data) = s(@)2. Goal is to find @ that minimizes expression3. @ in 1 known as "Least Squares Estimator of @" Properties of Estimators (particular to some, not given for all) 1. Linearity: 2. Unbiasedness: 3. Minimum Variance (of estimator): Best Linear Unbiased Estimator(BLUE) Proof that `Y is BLUE If Y~N(@, sig2) => `Y~ Matrix Notation for Estimation Estimating sig2 Chi-squared Distribution Wald Statistic Matrix Chi-Square: X2(m) Ybar = ^mu = (1/n)sum(Yi), where Yi~N(mu,sig2) s2 = ^sig = [sum(Yi - Ybar)2]/(n - 1), where Yi~N(mu,sig2) Show E(s2) = sig2, that is show that s2 is an unbiased estimator of population variance. T-distribution t = (Ybar - mu)/[s/sqrt(n)] = (Ybar - mu)/se(Ybar)~tn-1Derivation: Properties of t distribution Confidence Interval Ingredients of Hypothesis Test Var(Ybar) = ^sig2/n = s2/n se(Ybar) = ^sig/sqrt(n) = s/sqrt(n) Elements of T distribution Let Y1...Yn be a random sample from a population Yi~N(mu,sig2) Interval Estimation Probability of rejecting Ho when it is true Rejection Rules Ho: mu = muo H1: mu > muo Reject Ho and accept H1:If p <= alpha and t >= tcFail to reject Ho:If p > alpha and t < tc Rejection Rules Ho: mu = muo H1: mu < muo Reject Ho and accept H1:If p <= alpha and t <= -tcFail to reject Ho:If p > alpha and t > -tc Rejection Rules Ho: mu = muo H1: mu not equal to muo "Two-tailed test" Authormattstam ID66061 Card SetEcon7630_Exam1b DescriptionExam 1 (part b) for graduate level Econometrics 1 at LSU during spring 2011. Notation: Use @ for theta. ^ or ` before parameter indicates hat and bar (ex: `@ is theta-bar). Updated2011-02-14T16:09:52Z Show Answers