Gram-Charlier Approximations Applied to t Ratios of k-Class Estimators - Sargan, J. D. (Econometrica, 1975)
This paper obtains Edgeworth or Gram-Charlier expansions for the t ratio of instrumental variable and k-class estimators, and uses them to give approximations to the confidence intervals obtained from these t ratios. These confidence intervals for large sample size are more accurate than the usual asymptotic confidence interval. Charlier expansions is applied to the t ratio of 2SLS and non-stochastic k-class estimators. Previous general theorems in this field, with the exception of those given by Chambers [2], such as those in [3] have assumed that the statistic has moments of appropriate orders. The theorem proved here assumes only that it can be expressed as a function of other variables with moments of all orders with appropriate properties in some neighborhood of the origin. It can be applied to a wide range of