Constructing smooth tests without estimating the eigenpairs of the limiting process
无需估计极限过程特征对的平滑检验构造
Based on the well known Karhunen–Loève expansion, it can be shown that many omnibus tests lack power against “high frequency” alternatives. The smooth tests of Neyman (1937) may be employed to circumvent this power deficiency problem. Yet, such tests may be difficult to compute in many applications. In this paper, we propose a more operational approach to constructing smooth tests. This approach hinges on a Fourier representation of the postulated empirical process with…