EconometricsChengyuan YinSchool of Mathematics
Econometrics Chengyuan Yin School of Mathematics
Econometrics11. Asymptotic Distribution Theory
Econometrics 11. Asymptotic Distribution Theory
PreliminaryThis and our class presentation will be amoderately detailed sketch of these results.More complete presentations appear in Chapter4 of your text. Please read this chapterthoroughly. We will develop the results that weneed as we proceed. Also, (I believe) that thistopic is the most difficult conceptually in thiscourse, so do feel free to ask questions in class
Preliminary This and our class presentation will be a moderately detailed sketch of these results. More complete presentations appear in Chapter 4 of your text. Please read this chapter thoroughly. We will develop the results that we need as we proceed. Also, (I believe) that this topic is the most difficult conceptually in this course, so do feel free to ask questions in class
Asymptotics:SettingMost modeling situations involve stochastic regressors,nonlinear models or nonlinear estimation technigues.The number of exact statistical results, such asexpected value or true distribution, that can beobtained in these cases is very low. We rely, instead,on approximate results that are based on what weknow about the behavior of certain statistics in largesamples. Example from basic statistics: What can wesay about 1/ We know axlot about : What do wreknow about its reciprocal?
Asymptotics: Setting Most modeling situations involve stochastic regressors, nonlinear models or nonlinear estimation techniques. The number of exact statistical results, such as expected value or true distribution, that can be obtained in these cases is very low. We rely, instead, on approximate results that are based on what we know about the behavior of certain statistics in large samples. Example from basic statistics: What can we say about 1/ We know a lot about . What do we know about its reciprocal? x x
ConvergenceDefinitions, kinds of convergence as n grows large:1. To a constant; example, the sample mean, x2. To a random variable; example, a tstatisticwith n -1 degrees of freedom
Convergence Definitions, kinds of convergence as n grows large: 1. To a constant; example, the sample mean, 2. To a random variable; example, a t statistic with n -1 degrees of freedom x