检验删失持续时间模型中的未观测异质性：EM方法
Testing for Unobserved Heterogeneity in Censored Duration Models: EM Approach
- Vancouver School of Economics（温哥华经济学院）
- University of British Columbia（不列颠哥伦比亚大学）
- DENTSU SOKEN INC.（电通素研株式会社）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对删失持续时间模型中的未观测异质性，提出一种EM检验方法，其临界值无需模拟或自举，模拟显示在样本量≥500时尺寸准确且功效优于似然比检验，并在心脏移植数据中拒绝同质性。
AI中文摘要：
在持续时间模型中忽略未观测异质性会偏差参数估计并使推断失效，但对其进行检验是非正则的：原假设位于参数空间的边界上，且某些参数在原假设下不可识别。这些特征使得标准渐近理论不适用。本文基于Li, Chen, and Marriott (2009)的EM方法，为删失Weibull持续时间模型中的未观测异质性开发了一种EM检验。检验统计量的渐近零分布等于max{0, N(0,1)}的平方，因此临界值既不需要模拟也不需要自举，且该检验适用于任意形式的协变量相关删失。蒙特卡洛模拟将EM检验与Cho和White (2010)的似然比检验（LRT）、信息矩阵检验和拉格朗日乘子检验进行了比较。EM检验在样本量为500或以上时经验尺寸接近名义水平，而LRT明显保守，其他检验则过度拒绝。其尺寸调整功效与LRT相当，且高于其他检验。由于尺寸调整需要知道数据生成过程，在实践中不可用，因此在实际应用中EM检验在大多数设计下比LRT具有更高的功效。在斯坦福心脏移植数据的应用中，EM检验在每个协变量设定下都拒绝了同质性，而LRT的结论取决于用户选择的可接受参数值集合和设定。
英文摘要：
Ignoring unobserved heterogeneity in duration models biases parameter estimates and invalidates inference, but testing for it is non-regular: the null hypothesis lies on the boundary of the parameter space and some parameters are unidentified under the null. These features render standard asymptotic theory inapplicable. This paper develops an EM test for unobserved heterogeneity in censored Weibull duration models, building on the EM approach of Li, Chen, and Marriott (2009). The test statistic has an asymptotic null distribution equal to the square of max{0, N(0,1)}, hence critical values require neither simulation nor bootstrap, and the test accommodates covariate-dependent censoring of arbitrary form. Monte Carlo simulations compare the EM test with the likelihood ratio test (LRT) of Cho and White (2010), information matrix tests, and Lagrange multiplier tests. The EM test has empirical size close to the nominal level for sample sizes of 500 or more, where the LRT remains markedly conservative and the other tests over-reject. Its size-adjusted power is comparable to that of the LRT and higher than that of the other tests. Because size adjustment requires knowledge of the data-generating process and is unavailable in practice, the EM test attains higher power than the LRT in most designs as the tests would actually be applied. In an application to the Stanford Heart Transplant data, the EM test rejects homogeneity in every covariate specification, whereas the LRT's conclusion depends on a user-chosen set of admissible parameter values and on the specification.
