论文标题
内核条件矩测试通过最大力矩限制
Kernel Conditional Moment Test via Maximum Moment Restriction
论文作者
论文摘要
我们提出了一个新的规范测试家族，称为内核条件力矩（KCM）测试。我们的测试建立在一个新的称为条件嵌入（cmme）的内核希尔伯特空间（RKHS）中的有条件矩限制的新颖表示。将条件矩限制转换为无条件对应物的连续体后，测试统计量被定义为RKHS单位球内的最大矩限制（MMR）。我们表明，MMR不仅完全表征了原始的条件矩限制，从而导致假设检验和参数估计的一致性，而且具有易于计算以及封闭形式的渐近分布的分析表达。我们的实证研究表明，与现有测试相比，KCM测试具有有希望的有限样本性能。
We propose a new family of specification tests called kernel conditional moment (KCM) tests. Our tests are built on a novel representation of conditional moment restrictions in a reproducing kernel Hilbert space (RKHS) called conditional moment embedding (CMME). After transforming the conditional moment restrictions into a continuum of unconditional counterparts, the test statistic is defined as the maximum moment restriction (MMR) within the unit ball of the RKHS. We show that the MMR not only fully characterizes the original conditional moment restrictions, leading to consistency in both hypothesis testing and parameter estimation, but also has an analytic expression that is easy to compute as well as closed-form asymptotic distributions. Our empirical studies show that the KCM test has a promising finite-sample performance compared to existing tests.
