标题： 混合LR-$C(α)$-型检验用于不规则假设、一般准则函数和错误设定的模型 显示英文标题

标题： Mixed LR-$C(α)$-type tests for irregular hypotheses, general criterion functions and misspecified models

摘要： 本文介绍了一种似然比（LR）类型的检验，该检验在极值估计设置中具有\(C(\alpha)\)类型过程的稳健性特性。 该检验统计量是通过对受限和非受限准则函数分别进行调整构建的，并且在最小条件下被证明是渐近无偏的。 它具有两个主要的稳健性特性。 首先，与标准LR型统计量不同，即使在模型误设的情况下，信息矩阵等式不成立时，其零假设渐近分布仍为卡方分布。 其次，它能够处理涉及约束参数空间的不规则假设，例如边界参数，仅依赖于扰动参数的根\(n\)一致估计量。 当模型正确设定，不存在边界约束，且参数通过极值估计量估计时，所提出的检验退化为标准的LR型统计量。 对ARCH模型的模拟，其中波动率参数被限制为非负，以及具有潜在单调递增风险函数的参数生存回归，表明我们的检验保持了准确的尺寸并表现出良好的功效。 对双向误差分量模型的实证应用显示，所提出的检验可以提供比传统\(t\)检验更有信息量的推断。 显示英文摘要

摘要： This paper introduces a likelihood ratio (LR)-type test that possesses the robustness properties of \(C(\alpha)\)-type procedures in an extremum estimation setting. The test statistic is constructed by applying separate adjustments to the restricted and unrestricted criterion functions, and is shown to be asymptotically pivotal under minimal conditions. It features two main robustness properties. First, unlike standard LR-type statistics, its null asymptotic distribution remains chi-square even under model misspecification, where the information matrix equality fails. Second, it accommodates irregular hypotheses involving constrained parameter spaces, such as boundary parameters, relying solely on root-\(n\)-consistent estimators for nuisance parameters. When the model is correctly specified, no boundary constraints are present, and parameters are estimated by extremum estimators, the proposed test reduces to the standard LR-type statistic. Simulations with ARCH models, where volatility parameters are constrained to be nonnegative, and parametric survival regressions with potentially monotone increasing hazard functions, demonstrate that our test maintains accurate size and exhibits good power. An empirical application to a two-way error components model shows that the proposed test can provide more informative inference than the conventional \(t\)-test.