Exact Tests and Confidence sets in Linear Regressions with Autocorrelated Errors
提出一种在具有一阶自回归高斯扰动项的线性回归中构建精确检验和置信集的通用方法，通过处理冗余参数问题，利用投影法得到回归系数的保守置信集，并给出自相关系数的精确置信集。
This article proposes a general method to build exact tests and confidence sets in linear regressions with first-order autoregressive Gaussian disturbances. Because of a nuisance parameter problem, we argue that generalized bounds tests and conservative confidence sets provide natural inference procedures in such a context. Given an exact confidence set for the autocorrelation coefficient, we describe how to obtain a similar simultaneous confidence set for the autocorrelation coefficient and any subvector of regression coefficient. Conservative confidence sets for the regression coefficients are then deduced by a projection method. For any hypothesis that specifies jointly the value of the autocorrelation coefficient and any set of linear restrictions on the regression coefficients, we get exact similar tests. For tesing linear hypotheses about the regression coefficients only, we suggest bounds-type procedures. Exact confidence sets for the autocorrelation coefficient are built by "inverting" autocorrelation tests. The method is illustrated with two examples. Copyright 1990 by The Econometric Society.