This paper proposes $\chi^2$ goodness-of-fit tests for checking conditional distribution model's specifications. The method involves partitioning the sample into classes based on a cross-classification of the dependent and explanatory variables, resulting in a contingency table with expected frequencies that are independent of the parameters in the model and equal to the product of the marginals. Test statistics are computed using the trinity of tests, based on the likelihood of grouped data, to test whether the expected frequencies satisfy the model's restrictions. We also present a Chernoff-Lehman result that enables us to derive the asymptotic distribution of a Wald statistic using the efficient raw data estimator. The asymptotic distribution of the test statistics remains the same even when partitions are sample-dependent. An algorithm is developed to control the number of observations per cell. Monte Carlo experiments demonstrate the proposed tests' excellent size accuracy and good power properties.

翻译：本文针对条件分布模型设定的检验，提出了基于$\chi^2$的拟合优度检验方法。该方法通过将因变量与解释变量进行交叉分类，将样本划分为若干类别，构建列联表。该列联表中的期望频数与模型参数无关，且等于各边缘频数的乘积。基于分组数据的似然函数，利用检验三位一体统计量计算检验统计量，以验证期望频数是否满足模型约束条件。此外，我们提出了一种Chernoff-Lehman结果，使得能够利用高效原始数据估计量推导瓦尔德统计量的渐近分布。即使划分方式依赖于样本，检验统计量的渐近分布也保持不变。我们开发了一种算法来控制每个单元格的观测数量。蒙特卡洛实验表明，所提出的检验具有优异的尺寸准确性和良好的检验功效。