Considered here is a hypothesis test for the coefficients in the change-plane regression models to detect the existence of a change plane. The test that is considered is from the class of test problems in which some parameters are not identifiable under the null hypothesis. The classic exponential average tests do not work well in practice. To overcome this drawback, a novel test statistic is proposed by taking the weighted average of the squared score test statistic (WAST) over the grouping parameter's space, which has a closed form from the perspective of the conjugate priors when an appropriate weight is chosen. The WAST significantly improves the power in practice, particularly in cases where the number of the grouping variables is large. The asymptotic distributions of the WAST are derived under the null and alternative hypotheses. The approximation of critical value by the bootstrap method is investigated, which is theoretically guaranteed. Furthermore, the proposed test method is naturally extended to the generalized estimating equation (GEE) framework, as well as multiple change planes that can test if there are three or more subgroups. The WAST performs well in simulation studies, and its performance is further validated by applying it to real datasets.

翻译：本文考虑对变平面回归模型中的系数进行假设检验，以检测变平面的存在性。所研究的检验属于一类特殊检验问题，其中某些参数在原假设下不可识别。经典的指数平均检验在实际应用中效果不佳。为克服这一缺陷，本文提出一种新颖的检验统计量：通过对分组参数空间上的平方得分检验统计量进行加权平均（WAST）。当选取适当权重时，该统计量可从共轭先验角度获得闭式解。WAST在实际应用中显著提升了检验功效，尤其在分组变量数量较多的情况下表现突出。本文推导了WAST在原假设和备择假设下的渐近分布，研究了基于自助法临界值的近似方法，并提供了理论保证。此外，所提出的检验方法可自然扩展至广义估计方程（GEE）框架，并能处理多个变平面的情形，从而检验是否存在三个或更多子群。模拟研究表明WAST表现优异，其在实际数据集中的应用进一步验证了该方法的有效性。