Fixed-smoothing asymptotics in the generalized empirical likelihood estimation framework
广义经验似然估计框架中的固定平滑渐近理论AI 解读 ↓
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广义经验似然估计框架中的固定平滑渐近理论
- 研究问题
- 对时间序列的连续更新和最大分块经验似然估计，固定平滑渐近理论如何改变估计量与设定检验的分布及有限样本近似？
- 方法与思路
- 作者分别研究连续更新 GMM、鞍点形式的连续更新估计及最大分块经验似然，推导固定平滑分布和检验临界值，并开展模拟与数据分析。
- 材料陈述的贡献
- 摘要称，部分估计量的极限分布经未知线性变换后为混合正态，相关检验具有非标准枢轴分布，模拟显示分布近似与水平控制改善。
- 阅读关注点
- 应区分三种估计量，核对固定平滑的具体设定、未知变换与枢轴化步骤，并检查效率、功效及检验水平比较所依赖的条件。
- 阅读边界
- 仅据所给出版社摘要；摘要未列出正则条件、平滑参数设置和数值结果，所述效率及功效比较不能直接推广至任意时间序列环境。
原文摘要
This paper concerns the fixed-smoothing asymptotics for two commonly used estimators in the generalized empirical likelihood estimation framework for time series data, namely the continuous updating estimator and the maximum blockwise empirical likelihood estimator. For continuously updating generalized method of moments (GMM) estimator, we show that the results for the two-step GMM estimator in Sun (2014a) continue to hold under suitable assumptions. For continuous updating estimator obtained through solving a saddle point problem (Newey and Smith, 2004) and the maximum blockwise empirical likelihood estimator (Kitamura, 1997), we show that their fixed-smoothing asymptotic distributions (up to an unknown linear transformation) are mixed normal. Based on these results, we derive the asymptotic distributions of the specification tests (including the over-identification testing and testing on parameters) under the fixed-smoothing asymptotics, where the corresponding limiting distributions are nonstandard yet pivotal. Simulation studies show that (i) the fixed-smoothing asymptotics provides better approximation to the sampling distributions of the continuous updating estimator and the maximum blockwise empirical likelihood estimator as compared to the standard normal approximation. The testing procedures based on the fixed-smoothing critical values are more accurate in size than the conventional chi-square based tests; (ii) the continuously updating GMM estimator is asymptotically more efficient and the corresponding specification tests are generally more powerful than the other two competitors. Finite sample results from an empirical data analysis are also reported.