Asymptotic Theory
M. Hashem Pesaran · Oxford University Press eBooks · 2015
Most econometric methods used in applied economics, particularly in time series econometrics, are asymptotic in the sense that they are likely to hold only when the sample size is ‘large enough’. This chapter briefly reviews the different concepts of asymptotic convergence used in mathematical statistics and discusses their applications to econometric problems. The discussions cover concepts of convergence of random variables; the relationships among modes of convergence; convergence in distribution; stochastic orders Op (·) and Op (·); the law of large numbers; central limit theorems; the case of dependent and heterogeneously distributed observations; and transformation of asymptotically normal statistics. Exercises are provided at the end of the chapter.