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A model specification test for the variance function in nonparametric regression

机译:非参数回归方差函数的模型规范测试

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摘要

The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted -distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The null asymptotic distribution of the test statistic is obtained and employed to approximate the critical values. Finite sample properties of the proposed test are numerically investigated in several Monte Carlo experiments. The developed results assume independent data. Their extension to dependent observations is also discussed.
机译:在完全非参数回归模型中考虑了对条件方差的参数形式测试的问题。基于在零假设和替代方案下构建的残留物的经验特征函数与替代方案之间的经验特征函数之间的测试统计学,并从理论上进行了研究。获得测试统计的空渐近分布,并采用以近似临界值。在几个蒙特卡罗实验中,在数值研究了所提出的测试的有限样本性质。开发结果假设独立数据。还讨论了他们对依赖观察的延伸。

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