Practical Small-Sample Asymptotics for Regression Problems
针对独立但未必同分布的随机变量和，推导了鞍点逼近公式，并推广到估计方程和多变量问题，用于精确近似回归系数的分布，特别适用于广义线性模型，并以逻辑回归实例展示了如何结合Gibbs抽样获得置信区间。
Abstract Saddlepoint approximations are derived for sums of independent, but not necessarily identically distributed random variables, along with generalizations to estimating equations and multivariate problems. These results are particularly useful for accurately approximating the distribution of regression coefficients. General formulas are given for the distribution of the coefficients arising out of a generalized linear model with both canonical and noncanonical link functions. We illustrate the case of logistic regression with a real data example and show how the Gibbs sampler may be used to obtain confidence sets for each regression parameter based on the saddlepoint approximation.