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Fixed-smoothing asymptotics in the generalized empirical likelihood estimation framework

机译：广义经验似然估计框架中的固定平滑渐近性

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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. (C) 2016 Elsevier B.V. All rights reserved.
机译：本文涉及时间序列数据的广义经验似然估计框架中两个常用估计的固定平滑渐近性，即连续更新估计和最大块式经验似然估计。对于持续更新的广义矩量法（GMM）估计器，我们表明Sun（2014a）中两步GMM估计器的结果在适当的假设下继续成立。对于通过求解鞍点问题（Newey和Smith，2004）和最大块式经验似然估计（Kitamura，1997）获得的连续更新估计量，我们证明了它们的固定平滑渐近分布（直至未知的线性变换）是混合的正常。基于这些结果，我们得出了在平稳平滑渐近状态下规格测试（包括过度识别测试和参数测试）的渐近分布，其中相应的极限分布是非标准的但很关键的。仿真研究表明（i）与标准正态近似相比，固定平滑渐近线提供了对连续更新估计量和最大逐块经验似然估计量的采样分布的更好近似。基于固定平滑临界值的测试程序比基于常规卡方检验的测试更加精确。 （ii）连续更新的GMM估算器在渐近效率上更高，并且相应的规格测试通常比其他两个竞争对手更强大。还报告了来自经验数据分析的有限样本结果。 （C）2016 Elsevier B.V.保留所有权利。

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