摘要翻译：
本文提出了一种新的、方便的基于MCMC输出的$chi^2$wald检验的假设检验方法。新的统计量可以解释为Wald检验的MCMC版本，它有几个重要的优点，使其在实际应用中非常方便。首先，它在不适当的先验分布下定义良好，避免了Jeffrey-Lindley悖论。其次，可以证明它的渐近分布服从$\chi^2$分布，从而可以很容易地从该分布中标定阈值。第三，利用马尔可夫链蒙特卡罗(MCMC)方法推导其统计误差。第四，最重要的是，它只基于从后验分布中抽取的后验MCMC随机样本。因此，它只是后验输出的副产品，非常容易计算。此外，在先验信息可用的情况下，对所提出的检验统计量导出了有限样本理论。最后，通过对经济和金融中广泛应用的潜变量模型的几个应用，说明了该检验的有效性。
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英文标题：
《A New Wald Test for Hypothesis Testing Based on MCMC outputs》
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作者：
Yong Li, Xiaobin Liu, Jun Yu and Tao Zeng
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最新提交年份：
2018
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
  In this paper, a new and convenient $\chi^2$ wald test based on MCMC outputs is proposed for hypothesis testing. The new statistic can be explained as MCMC version of Wald test and has several important advantages that make it very convenient in practical applications. First, it is well-defined under improper prior distributions and avoids Jeffrey-Lindley's paradox. Second, it's asymptotic distribution can be proved to follow the $\chi^2$ distribution so that the threshold values can be easily calibrated from this distribution. Third, it's statistical error can be derived using the Markov chain Monte Carlo (MCMC) approach. Fourth, most importantly, it is only based on the posterior MCMC random samples drawn from the posterior distribution. Hence, it is only the by-product of the posterior outputs and very easy to compute. In addition, when the prior information is available, the finite sample theory is derived for the proposed test statistic. At last, the usefulness of the test is illustrated with several applications to latent variable models widely used in economics and finance.
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PDF链接：
https://arxiv.org/pdf/1801.00973