Ordered Regressions
研究了当多个回归函数在协变量取值范围内存在顺序关系时，如何进行有效的约束估计和检验，通过二次规划或半无限规划估计参数，并提出了距离型顺序检验，模拟和听力损失研究应用显示能显著改善均方误差和检验功效。
Abstract There are often situations where two or more regression functions are ordered over a range of covariate values. In this paper, we develop efficient constrained estimation and testing procedures for such models. Specifically, necessary and sufficient conditions for ordering generalized linear regressions are given and shown to unify previous results obtained for simple linear regression, for polynomial regression and in the analysis of covariance models. We show that estimating the parameters of ordered linear regressions requires either quadratic programming or semi‐infinite programming, depending on the shape of the covariate space. A distance‐type test for order is proposed. Simulations demonstrate that the proposed methodology improves the mean square error and power compared with the usual, unconstrained, estimation and testing procedures. Improvements are often substantial. The methodology is extended to order generalized linear models where convex semi‐infinite programming plays a role. The methodology is motivated by, and applied to, a hearing loss study.