This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Parametric Inference – II KullbackLeibler distance )) f(x; ), D(f(x; for ) , D( write shall we , , For 0. f) D(f, and g) D(f, shown that be can It g(x) f(x) f(x)ln g) D(f, be to defined is g and f between distance Leibler  Kullback the s pdf' are g and f If ψ θ ψ θ ψ θ Θ ∈ = ≥ = ∫ dx Identifiability ons. distributi different to correspond parameter the of values different that means This ) , D( that implies if le identifiab be to said is model The ≠ ℑ ψ θ ψ θ Consistency of MLE  = = = →  = = ∑ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ when maximized is which ) , ( ) ; ( ) ; ( ln E Now, ) ; ( ) ; ( ln E ) ( M By WLLN, ). (w.r.t constant a is ) ( and )) ( ) ( ( ) ( M since ) ( M maximizing to equivalent is ) ( Maximizing ) ; ( ) ; ( ln 1 ) ( M Define . of value true the denote Let P n * 1 n n n 1 n D X f X f X f X f l l l n l X f X f n i i i i n n n n i i i Consistency of MLE Equivariance of the MLE...
View
Full
Document
This note was uploaded on 05/07/2009 for the course FIN AMDA taught by Professor Proflaha during the Spring '09 term at Indian Institute Of Management, Ahmedabad.
 Spring '09
 ProfLaha

Click to edit the document details