In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a performance measurement in all possible modeling scenarios. Thus, in theory, an irrelevant feature is equivalent to a dummy player in the game, which contributes nothing to all modeling situations. The hypothesis test of zero mean contribution is the rule to decide a feature is irrelevant or not. In our mechanism design, the end goal perfectly matches the expected model performance with the expected sum of individual marginal effects. Within a class of noninformative likelihood among all modeling opportunities, the matching equation results in a specific valuation for each feature. After estimating the valuation and its standard deviation, we drop any candidate feature if its valuation is not significantly different from zero. In the simulation studies, our new approach significantly outperforms several popular methods used in practice, and its accuracy is robust to the choice of the payoff function.
翻译:在构建一个计量经济学或统计模型时,我们从许多候选人中选择相关的特征或变量。设置了一个联盟游戏,研究选择问题,即参与者是候选人,而报酬函数是所有可能的模型情景中的绩效衡量。因此,理论上,一个无关的特征相当于游戏中的假玩家,这对所有模型情况都无任何帮助。关于零平均贡献的假设测试是确定某个特征的规则是无关紧要的或不是的。在我们的机制设计中,最终目标完全匹配预期模型性能和个人边际效应的预期总和。在所有模型机会中的非信息可能性类别中,匹配方程的结果是每个特征的具体估值。在估算估值及其标准偏差之后,我们放弃任何候选人特征,如果其估值与零差别不大。在模拟研究中,我们的新方法大大超越了实践中使用的几种流行方法,其准确性对于选择报酬功能十分有力。