Distribution-free specification tests of conditional models
提出一类渐近无分布的设定检验方法，用于检验参数条件分布的正确性，通过鞅变换构造综合检验和方向检验，并以条件正态性检验为例展示其有效性。
This article proposes a class of asymptotically distribution-free specification tests for parametric conditional distributions. These tests are based on a martingale transform of a proper sequential empirical process of conditionally transformed data. Standard continuous functionals of this martingale provide omnibus tests while linear combinations of the orthogonal components in its spectral representation form a basis for directional tests. Finally, Neyman-type smooth tests, a compromise between directional and omnibus tests, are discussed. As a special example we study in detail the construction of directional tests for the null hypothesis of conditional normality versus heteroskedastic contiguous alternatives. A small Monte Carlo study shows that our tests attain the nominal level already for small sample sizes.