A CONSISTENT DIAGNOSTIC TEST FOR REGRESSION MODELS USING PROJECTIONS
利用投影的回归模型一致诊断检验AI 解读 ↓
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利用投影的回归模型一致诊断检验
- 研究问题
- 如何检验参数回归模型的拟合设定，缓解维数灾难和调节参数主观选择的问题，并允许条件异方差等高阶依赖？
- 方法与思路
- 作者利用基于投影的残差标记经验过程构造检验，以自助法处理依赖数据生成过程的零分布，并构造最小距离估计。
- 材料陈述的贡献
- 摘要称，检验一致且可检测参数速率的局部备择，自助检验对所述高阶依赖稳健，配套估计量一致且渐近正态。
- 阅读关注点
- 应核对投影与统计量的构造、局部备择定义、自助法有效性的依赖条件，以及避免调节参数选择的实际实现方式。
- 阅读边界
- 仅据 RePEc 所载出版社摘要；摘要未说明完整正则条件或模拟数值，所谓稳健性不能解释为允许任意形式的数据依赖。
原文摘要
This paper proposes a consistent test for the goodness-of-fit of parametric regression models that overcomes two important problems of the existing tests, namely, the poor empirical power and size performance of the tests due to the curse of dimensionality and the subjective choice of parameters such as bandwidths, kernels, and integrating measures. We overcome these problems by using a residual marked empirical process based on projections (RMPP). We study the asymptotic null distribution of the test statistic, and we show that our test is able to detect local alternatives converging to the null at the parametric rate. It turns out that the asymptotic null distribution of the test statistic depends on the data generating process, and so a bootstrap procedure is considered. Our bootstrap test is robust to higher order dependence, in particular to conditional heteroskedasticity. For completeness, we propose a new minimum distance estimator constructed through the same RMPP as in the testing procedure. Therefore, the new estimator inherits all the good properties of the new test. We establish the consistency and asymptotic normality of the new minimum distance estimator. Finally, we present some Monte Carlo evidence that our testing procedure can play a valuable role in econometric regression modeling.The author thanks Carlos Velasco and Miguel A. Delgado for useful comments. The paper has also benefited from the comments of two referees and the co-editor. This research was funded by the Spanish Ministry of Education and Science reference number SEJ2004-04583/ECON and by the Universidad de Navarra reference number 16037001.