ACS Regression theory

ACS Regression theory

1. Basic Asymptotic Theory

   • causality
   • Convergence of serries
     • Stochastic
       • Plim:
     • deterministic
       • the other one..../
   • Limit Therems
     • LLN
       • IF an IID variable X has a finite mean U < infinity. the sample mean ... as N goes to infinity
     • CLT
       • The sample mean of an IID variable will be N with mean 0 and Var theta after demeaning.
     • Continuous Mapping Theorem
       • IF xn -p--> a then g(Xn) --p--> g(a)

2. Ordinary Least Squares

   • Assumptions
     • E(x,u) = 0: rank(x'x) = k+1 E(u^2x'x) = @^2 E(x'x)
       • Uncorrelatedness
   • Desirable properties
     • 1:Unbiased:consistent, 2:if biased converges quickly, 3Small root mse in finite samples, Robust to outliers. robust to misspecicfication. Easy to use;++