Accurate Directional Inference for Vector Parameters in Linear Exponential Families
针对线性指数族中带有限维冗余参数的向量参数，提出一种基于高阶渐近理论的方向检验，其p值通过一维积分计算，在列联表和逻辑回归等离散模型及协方差选择等高维场景中精度优于传统似然比检验。
We consider inference on a vector-valued parameter of interest in a linear exponential family, in the presence of a finite-dimensional nuisance parameter. Based on higher-order asymptotic theory for likelihood, we propose a directional test whose p-value is computed using one-dimensional integration. The work simplifies and develops earlier research on directional tests for continuous models and on higher-order inference for discrete models, and the examples include contingency tables and logistic regression. Examples and simulations illustrate the high accuracy of the method, which we compare with the usual likelihood ratio test and with an adjusted version due to Skovgaard. In high-dimensional settings, such as covariance selection, the approach works essentially perfectly, whereas its competitors can fail catastrophically.