Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis
在零均值AR(1)模型中推导单位根假设检验的渐近功效上界，使用实验极限方法，将误差分布视为未知无穷维 nuisance 参数，并探讨对称性假设下适应性检验的可能性。
This paper derives asymptotic power envelopes for tests of the unit root hypothesis in a zero-mean AR(1) model. The power envelopes are derived using the limits of experiments approach and are semiparametric in the sense that the underlying error distribution is treated as an unknown infinite-dimensional nuisance parameter. Adaptation is shown to be possible when the error distribution is known to be symmetric and to be impossible when the error distribution is unrestricted. In the latter case, two conceptually distinct approaches to nuisance parameter elimination are employed in the derivation of the semiparametric power bounds. One of these bounds, derived under an invariance restriction, is shown by example to be sharp, while the other, derived under a similarity restriction, is conjectured not to be globally attainable.