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摘要翻译：
随机系数模型是线性回归模型的一个扩展，它通过将回归系数建模为随机变量来考虑种群中未观察到的异质性。在给定数据的情况下，统计上的挑战是恢复随机系数的联合密度信息，这是一个多变量和不适定的问题。由于维数的诅咒和不适定性，节点密度的逐点非参数估计是困难的，而且收敛速度慢。然而，更大的特征，如沿某个方向密度的增加或一个很好的强调模式，可以通过统计测试从数据中更容易地检测出来。在本文中，我们遵循这一策略，并构造测试和置信度的定性特征，如增加，减少和模式。我们提出了一种基于聚合单个测试的多重测试方法，该方法旨在提取固定尺度和方向上的形状信息。利用多元经验过程高斯近似的最新工具，我们导出了临界值的表达式。我们将我们的方法应用于模拟和真实数据。
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英文标题：
《Tests for qualitative features in the random coefficients model》
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作者：
Fabian Dunker, Konstantin Eckle, Katharina Proksch, Johannes
Schmidt-Hieber
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最新提交年份：
2018
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分类信息：
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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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：
The random coefficients model is an extension of the linear regression model that allows for unobserved heterogeneity in the population by modeling the regression coefficients as random variables. Given data from this model, the statistical challenge is to recover information about the joint density of the random coefficients which is a multivariate and ill-posed problem. Because of the curse of dimensionality and the ill-posedness, pointwise nonparametric estimation of the joint density is difficult and suffers from slow convergence rates. Larger features, such as an increase of the density along some direction or a well-accentuated mode can, however, be much easier detected from data by means of statistical tests. In this article, we follow this strategy and construct tests and confidence statements for qualitative features of the joint density, such as increases, decreases and modes. We propose a multiple testing approach based on aggregating single tests which are designed to extract shape information on fixed scales and directions. Using recent tools for Gaussian approximations of multivariate empirical processes, we derive expressions for the critical value. We apply our method to simulated and real data.
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PDF链接：
https://arxiv.org/pdf/1704.01066
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