We propose a method for testing hypothesis on parametric family of transition probabilities of a Markov sequence, when the asymptotic distribution of the empirical processes involved is, largely, independent from the specific form of the parametric family. We first consider function-parametric empirical process for the Markov sequence and describe its weak limit as a certain projection. Then we establish equivalence between testing different families of transition probabilities and show how the empirical process for one testing problem can be transformed into empirical process in another testing problem. This creates wide equivalence classes and allows distribution free testing.

当所涉及的经验过程的渐近分布在很大程度上独立于参数族的特定形式时，我们提出了一种检验关于马尔可夫序列的参数族的转移概率的假设的方法。我们首先考虑马尔可夫序列的函数参数经验过程，并将其弱极限描述为某个投影。然后，我们建立了测试不同过渡概率族之间的等价关系，并展示了如何将一个测试问题的经验过程转化为另一测试问题的经验过程。这将创建广泛的等效类，并允许免费分发测试。