# 论坛讲座

## 2020-04-28

Junnan He （Sciences Po， Econ）

A Test for Sparsity

2020年4月29日（周三）10:00-11:30

Webex会议链接：

https://pku.webex.com.cn/pku/j.php?MTID=m061e45780c4a11f0976308c1d19650e3

会议密码：MgFB333SKun

Many properties of sparse estimators rely on the assumption that the underlying data generating process is sparse. When this assumption does not hold, a sparse estimator can perform worse than a non-sparse one such as the ridge estimator. We propose a test of sparsity for linear regression models. Our null hypothesis is that the number of non-zero parameters does not exceed a small preset fraction of the total number of parameters. It can be interpreted as a family of generating distributions where each parameter equals zero with a large probability. As the alternative, all parameters are nonzero and of order $1/\sqrt p$ for all $p$ number of parameters. Formally the alternative is a normal distribution, the maximum entropy distribution with zero mean and the variance determined by the ANOVA identity. We derive a test statistic using the theory of robust statistics. This statistic is minmax-optimal when the design matrix is orthogonal, and can be used for general design matrices as a conservative test. As an empirical illustration, we apply our test to an estimated Almost Ideal Demand System and conclude that the vector of cross-price parameters is sparse.

Junnan He is an Assistant Professor at Sciences Po. His research interests lie in econometrics and decision theory. Primarily, he works on model sparsity, variable selection, and stochastic choice models.

2018年10月，金沙棋牌官方版、国家发展研究院和新结构经济学研究院达成框架合作协议，约定采用轮流主持的方式共同举办工作坊，正式建立了科研领域的交流创新合作机制。2019年，根据协议，先后成立了七个工作坊：政治经济学工作坊；国际经济学与实证产业组织工作坊；宏观经济学工作坊；微观理论经济学工作坊；计量经济学和大数据分析工作坊；劳动-健康经济学工作坊和发展与公共财政工作坊。2019年七个工作坊共计举办127场活动，这些活动为广大师生提供了良好的国内外一流学术交流平台，促进了学院之间的学术资源整合和人才培养，提升了广大师生和经济学领域的研究水平。

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