We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a structural representation of the limit experiment and exploiting invariance relationships therein, we construct invariant point-optimal tests for the regression coefficient of interest. This approach naturally leads to a family of feasible tests based on the component-wise ranks of the innovations that can gain considerable power relative to existing tests under non-Gaussian innovation distributions, while behaving equivalently under Gaussianity. When an i.i.d. assumption on the innovations is appropriate for the data at hand, our tests exploit the efficiency gains possible. Moreover, we show by simulation that our test remains well behaved under some forms of conditional heteroskedasticity.

我们使用高度持久的预测器解决了二元回归问题中的半参数效率问题，其中创新的联合分布被视为无限维的有害参数。使用极限实验的结构表示并利用其中的不变关系，我们为感兴趣的回归系数构建不变点最优检验。这种方法自然会导致一系列可行的测试，这些测试基于创新的组件级别，相对于非高斯创新分布下的现有测试可以获得相当大的功率，同时在高斯下表现相同。当创新的独立同分布假设适合手头的数据时，我们的测试会利用可能的效率增益。而且，