There has been much attention on the de-biased or de-sparsified Lasso. The Lasso is very useful in high-dimensional settings. However, it is well known that the Lasso produces biased estimators. Therefore, several authors proposed the de-biased Lasso to fix this drawback and carry out statistical inferences based on the de-biased Lasso estimators. The de-biased Lasso needs desirable estimators of high-dimensional precision matrices. Thus, the research is almost limited to linear regression models with some restrictive assumptions, generalized linear models with stringent assumptions, and the like. To our knowledge, there are a few papers on linear regression models with group structure, but no result on structured nonparametric regression models such as varying coefficient models. We apply the de-biased group Lasso to varying coefficient models and examine the theoretical properties and the effects of approximation errors involved in nonparametric regression. The results of numerical studies are also presented.

中文翻译：

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变系数模型的去偏组 Lasso 估计

去偏差或去稀疏化的 Lasso 受到了很多关注。Lasso 在高维设置中非常有用。然而，众所周知，套索会产生有偏估计。因此，几位作者提出了去偏置的 Lasso 来解决这个缺点，并基于去偏置的 Lasso 估计量进行统计推断。去偏置 Lasso 需要高维精度矩阵的理想估计器。因此，研究几乎仅限于具有一些限制性假设的线性回归模型、具有严格假设的广义线性模型等。据我们所知，有一些关于具有组结构的线性回归模型的论文，但没有关于结构化非参数回归模型（例如变系数模型）的结果。我们将去偏置组 Lasso 应用于不同的系数模型，并检查理论属性和非参数回归中涉及的近似误差的影响。还介绍了数值研究的结果。