In this dissertation, we explore the use of three different analytical techniques for approximating the finite-sample properties of estimators and test statistics. These techniques are the saddlepoint approximation, the large-n approximation and the small-disturbance approximation. The first of these enables us to approximate the complete density or distribution function for a statistic of interest, while the other two approximations provide analytical results for the first few moments of the finite-sample distribution. We consider a range of interesting estimation and testing problems that arise in econometrics and empirical economics. Saddlepoint approximations are used to determine the distribution of the half-life estimator that arises in the empirical purchasing power parity literature, and to show that its moments are undefined. They are also applied to the problem of obtaining accurate critical points for the Anderson-Darling goodness-of-fit test. The large-n approximation is used to study the first two moments of the MLE in the binary Logit model. Finally, we use small-disturbance approximations to examine the bias and mean squared error of some commonly used price index numbers, when the latter are viewed as point estimators.

In this dissertation, we explore the use of three different analytical techniques for approximating the finite-sample properties of estimators and test statistics. These techniques are the saddlepoint approximation, the large-n approximation and the small-disturbance approximation. The first of these enables us to approximate the complete density or distribution function for a statistic of interest, while the other two approximations provide analytical results for the first few moments of the finite-sample distribution. We consider a range of interesting estimation and testing problems that arise in econometrics and empirical economics. Saddlepoint approximations are used to determine the distribution of the half-life estimator that arises in the empirical purchasing power parity literature, and to show that its moments are undefined. They are also applied to the problem of obtaining accurate critical points for the Anderson-Darling goodness-of-fit test. The large-n approximation is used to study the first two moments of the MLE in the binary Logit model. Finally, we use small-disturbance approximations to examine the bias and mean squared error of some commonly used price index numbers, when the latter are viewed as point estimators.