Testing when a parameter is on the boundary of the maintained hypothesis
Testing when a parameter is on the boundary of the maintained hypothesis
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DOI：
10.1111/1468-0262.00210
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发表时间：
2001-05-01
期刊：
影响因子：
6.1
通讯作者：
Andrews, DWK
中科院分区：
文献类型：
--
作者：
Andrews, DWK
本文考虑测试问题的几个标准的正则性条件不成立。我们考虑的情况下，（i）零假设中的参数向量可能位于边界上：维持假设和（ii）有可能是一个滋扰参数，出现在备择假设，但不是在零。本文建立了这种情况下拟似然比、重标拟似然比、Wald检验和score检验的渐近零分布和局部替代分布。结果适用于基于各种极值估计量的检验，并适用于各种模型。本文中处理的示例包括：（i）在GARCH（1，1）回归模型和（ii）在随机系数回归模型中某些随机系数的方差等于零的零假设检验，（可能）相关随机系数。
This paper considers testing problems where several of the standard regularity conditions fail to hold. We consider the case where (i) parameter vectors in the null hypothesis may lie on the boundary of the: maintained hypothesis and (ii) there mas be a nuisance parameter that appears under the alternative hypothesis, but not under the null. The paper establishes the asymptotic null and local alternative distributions of quasi-likelihood ratio, rescaled quasi-likelihood ratio, Wald, and score tests in this case. The results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models.Examples treated in the paper are: (i) tests of the null hypothesis of no conditional heteroskedasticity in a GARCH(1,1) regression model and (ii) tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with (possibly) correlated random coefficients.