THE FINITE-SAMPLE DENSITY OF THE SUFFICIENT STATISTIC AND RELATED TESTS IN A GAUSSIAN AUTOREGRESSION
推导了一阶高斯自回归模型中最小充分统计量的精确有限样本联合密度，进而得到自相关系数及其学生化t比率的精确密度，解决了此前仅知渐近结果的问题。
A first-order Gaussian autoregressive model is considered. The exact finite-sample joint density of the minimal sufficient statistic is derived, for any value of the autoregressive parameter. This allows us to derive explicitly the exact density of the autocorrelation coefficient and its Studentized t-ratio, whose densities were available only in the asymptotic case and not for all values of the parameter and the statistic. This article also demonstrates how to solve a general problem in statistical distribution theory (well beyond the specific case of autoregressive models), that of inverting confluent characteristic functions in multiple variables.