Some of the statistical aspects of estimating travel-time anomalies and station corrections are considered. In order to estimate these quantities using earthquake data the events themselves must first be located. We investigated the use of the Gauss-Newton iterative technique to obtain a least-squares epicenter location employing Monte Carlo methods. Results of these studies indicate that the Gauss-Newton process converges to an absolute minimum and that confidence ellipses computed by linear techniques are reliable for reasonable networks of well-distributed stations. Also the Monte Carlo studies indicate that a least-squares solution may be inaccurate if appreciable travel-time anomalies or station-error means exist. We then expanded the location procedure to include the estimation of travel-time anomalies and station corrections. In order to obtain these estimates data from some 278 large earthquakes were analyzed by using a modified Seidel iterative process.