Nonnormal Linear Regression; An Example of Significance Levels in High Dimensions
针对非正态线性模型，提出一种条件方法来评估单个参数的观测显著性水平，并用重要性抽样改进近似精度，同时推广到实际枢轴量和贝叶斯推断。
Analysis of nonnormal linear models leads to an initial conditioning on the standardized residuals, giving an unnormed density on Rk, where k is the number of parameters. To obtain an observed level of significance for a single parameter it is then necessary to calculate a marginal probability, thus requiring integration in k dimensions. In this paper a conditional approach to evaluating the observed level of significance is developed, and an importance sampling technique is used to improve the approximation and assess the accuracy of the conditional approximation to the marginal observed level. A further approximation based on the invariant version (Fraser, 1990) of the Lugannam & Rice (1980) formula is also proposed. The approach extends to the evaluation of real pivots and to Bayesian inference for a single parameter component.