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摘要翻译：
非线性模型的一个基本问题是极大似然估计不能保证存在。尽管不存在是二元选择文献中一个众所周知的问题，但它也给其他模型带来了重大挑战，而且在更一般的环境中也没有得到很好的理解。这些挑战只在具有许多固定效果和其他高维参数的模型中被放大。我们通过研究用于估计一类广义线性模型的（伪）极大似然估计量的估计存在的条件来解决当前围绕这一主题的模糊性。我们证明了当这些条件不成立时，这些GLM估计中的一些，但不是全部，仍然可以提供至少一些线性参数的一致估计。我们还演示了如何在具有高维参数的模型中验证这些条件，如具有多级固定效应的面板数据模型。
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英文标题：
《Verifying the existence of maximum likelihood estimates for generalized
linear models》
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作者：
Sergio Correia, Paulo Guimar\~aes, and Thomas Zylkin
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最新提交年份：
2021
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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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英文摘要：
A fundamental problem with nonlinear models is that maximum likelihood estimates are not guaranteed to exist. Though nonexistence is a well known problem in the binary choice literature, it presents significant challenges for other models as well and is not as well understood in more general settings. These challenges are only magnified for models that feature many fixed effects and other high-dimensional parameters. We address the current ambiguity surrounding this topic by studying the conditions that govern the existence of estimates for (pseudo-)maximum likelihood estimators used to estimate a wide class of generalized linear models (GLMs). We show that some, but not all, of these GLM estimators can still deliver consistent estimates of at least some of the linear parameters when these conditions fail to hold. We also demonstrate how to verify these conditions in models with high-dimensional parameters, such as panel data models with multiple levels of fixed effects.
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PDF链接：
https://arxiv.org/pdf/1903.01633
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