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高维广义线性模型的拟合优度检验AI 解读

Summary We propose a family of tests to assess the goodness of fit of a high dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and interaction effects, or for testing the significance of groups of variables. The methodology is based on extracting left-over signal in the residuals from an initial fit of a generalized linear model. This can be achieved by predicting…

高维模型的半参数效率界AI 解读

Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper, we propose a framework for obtaining semiparametric efficiency bounds for sparse high-dimensional models, where the dimension of the parameter is larger than the sample size. We adopt a semiparametric point of view: we concentrate on one-dimensional functions of a high-dimensional parameter. We follow two different approaches to reach the lower…