This paper proposes efficient tests for quantile parameter instability in parametric and semiparametric setups. In each setup, various types of unstable parameter processes are examined such as single structural break, multiple structural breaks, and random parameters, and the optimal test is suggested for each unstable process. In a parametric model, tick-exponential family of distributions is used to construct the likelihood ratio tests. The suggested tests have the best asymptotic weighted average power if the likelihood function is correctly specified and are asymptotically correct-sized even under misspecification. In a semiparametric setup in which the underlying distribution is unknown but is treated as an infinite-dimensional nuisance parameter, we show that semiparametric efficient tests are adaptive if the error term is conditionally iid. Non-adaptive efficient tests are suggested under weaker conditions as well. Monte Carlo simulation shows that the proposed tests have better finite sample powers than the existing tests under various circumstances.

中文翻译：

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条件分位数模型中参数破坏过程的最佳测试

本文针对参数和半参数设置中的分位数参数不稳定性提出了有效的测试方法。在每种设置中，都会检查各种类型的不稳定参数过程，例如单个结构破坏，多个结构破坏和随机参数，并建议针对每个不稳定过程的最佳测试。在参数模型中，刻度指数分布族用于构造似然比检验。如果正确指定了似然函数，并且即使在错误指定的情况下，渐近正确大小，建议的测试也具有最佳渐近加权平均功效。在其中基础分布未知但被视为无穷大扰动参数的半参数设置中，我们表明，如果误差项是有条件的，则半参数有效检验是自适应的IID。建议在较弱的条件下进行非自适应高效测试。蒙特卡洛模拟显示，在各种情况下，所提出的测试具有比现有测试更好的有限样本能力。