Browsing by Subject "asymptotic normality"

The phrase 'central limit theorem' has commonly come to stand for a result where partial sums of random variables converge to a gaussian random variable in the sense of distribution. Theorems of this nature readily yield applications to statistics and econometrics since they form the theoretical basis of approximating the sampling distribution of a given test statistic when the exact distribution may be intractable or otherwise infeasible to be retrieved. Faced with such a situation, a researcher can instead ask whether the test statistic, or a certain transformation of it, converges in distribution as the sample size grows without bound. If the answer is in the affirmative, then one may in a principled manner approximate the distribution of the finite-sample statistics with that of the limit distribution such that the approximation can be made in some sense arbitrarily good by sufficient increases in the sample size. Naturally, similar procedures apply in the case of estimators. These asymptotic normality results for econometric estimators, as they are called, require differing conditions to be satisfied depending on the nature of the data-generating process where the observations are thought to originate from. This thesis examines a selection of foundational central limit theorems in the cases of I.I.D., independent, D.I.D., and dependent data-generating processes and presents examples of their econometric applications, primarily to deduce asymptotic normality for a selection of key econometric estimators.