Abstract This paper considers conditional moment models where the parameters of interest include both finite-dimensional parameters and unknown functions. We propose sup-Wald, sup-quasi-likelihood ratio and sup-Lagrange multiplier statistics for testing functionals restrictions uniformly over the support for both finite and infinite dimensional components of the parameters. The trinity of three statistics holds because they are asymptotically equivalent and can be strongly approximated by a sequence of chi-squared processes. Based on these results, we can, for instance, construct confidence intervals and uniform confidence bands for the unknown functions, the partial derivatives of the unknown functions and the functional combinations of the two parameters.

中文翻译：

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条件矩模型函数的三位一体检验

摘要 本文考虑了条件矩模型，其中感兴趣的参数包括有限维参数和未知函数。我们提出了 sup-Wald、sup-quasi-likelihood ratio 和 sup-Lagrange 乘数统计，用于在对参数的有限维和无限维分量的支持上一致地测试泛函限制。三个统计量的三位一体是成立的，因为它们是渐近等价的，并且可以通过一系列卡方过程进行强烈近似。例如，基于这些结果，我们可以为未知函数、未知函数的偏导数和两个参数的函数组合构建置信区间和统一置信带。