1 Introduction Fama[1970] says a market in which prices always ”fully reflect” available information is called ”efficient”, that is, successive price changes (or more usually, successive one-period returns) are independent. In other words, if the flow ...
Econometrics Theory 1 Linear Regression Model 1.1 Basics and estimation Let us conside a simple linear regression model below. yt= b1+ b2xt+ ut; for t= 1;;n This function is mapping fromxt toyt, that is,xt ! yt. Here we call each variables,yt as explained vari...
Asymptotic Noramlity of Maximum Likelihood Estimator and the distribution of Lagrange Multiplier and Likelihood Ratio test statistic This article gives the proof of the asymptotic normality of maximum likelihood estimator and the distribution of LM and LR stat...
Proof of Helly-Bray Theorem, Continuity Theorem and Cram´er -Wold Theorem Theorem(Helly-Bray)Let g(x) be bounded,continuous function and assume thatfFn(x)g is a sequence of uniformly bounded,non decreasing distribution functions which converges to F(x) at all ...
Contract Theory 1 Adverse Selection Let us set up the problem as follows. The set of supplier’s type;Q = fq0;q1g, where 0< q0 < q1. Here supplier of typeq0 is superior, and supplier of typeq1 is inferior. And assume that the true type of supplier is only know...
Proof of Useful Propositions as to Stochastic Convergence Proposition(a)LetfYYng be a sequence of n 1 random vectors withYYn d ! Y.SupposefXXng is a sequence of n 1 random vectors such that(XXn YYn) p ! 0Then XXn converges in distribution toYY. Proof Denote th...