We propose a cross-classification rule for the dependent and explanatory variables resulting in a contingency table such that the classical trinity of chi-square statistics can be used to check for conditional distribution specification. The resulting Pearson statistic is equal to the Lagrange multiplier statistic. We also provide a Chernoff-Lehmann result for the Pearson statistic using the raw data maximum likelihood estimator, which is applied to show that the corresponding limiting distribution of the Wald statistic does not depend on the number of parameters. The asymptotic distribution of the proposed statistics does not change when the grouping is data dependent. An algorithm allowing to control the number of observations per cell is developed. Monte Carlo experiments provide evidence of the excellent size accuracy of the proposed tests and their good power performance, compared to omnibus tests, in high dimensions.

翻译：我们提出了一种对因变量和解释变量进行交叉分类的规则，从而生成列联表，使得经典的卡方统计量三元组可用于检验条件分布的设定。所得到的皮尔逊统计量等于拉格朗日乘子统计量。我们还为基于原始数据最大似然估计的皮尔逊统计量提供了一个Chernoff-Lehmann结果，该结果被用于证明对应的沃尔德统计量的极限分布不依赖于参数数量。当分组依赖于数据时，所提出统计量的渐近分布保持不变。我们开发了一种算法，可控制每个单元格的观测数量。蒙特卡洛实验表明，与综合检验相比，所提出的检验在高维场景下具有极好的大小准确性及良好的功效表现。