High Dimensional Inference in Partially Linear Models
High Dimensional Inference in Partially Linear Models
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DOI：
10.2139/ssrn.3015397
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发表时间：
2017-08
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影响因子：
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通讯作者：
Ying Zhu;Zhuqing Yu;Guang Cheng
中科院分区：
文献类型：
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作者：
Ying Zhu;Zhuqing Yu;Guang Cheng
我们提出了两个半参数版本的去偏Lasso过程的模型$Y_i = X_i\beta_0 + g_0（Z_i）+ \xB_i$，其中$\beta_0 $是高维的，但稀疏（精确或近似）。这两个版本被证明具有相同的渐近正态分布，不需要最小信号条件的任何组件的统计推断$\beta_0$。当$Z_i$是高维函数时，只要函数类$E（X_{ij}| Z_i）$s和$E（Y_i| Z_i）$属于表现出某些稀疏性特征，例如，稀疏加法分解结构。我们进一步发展了一个基于乘数自助法的同步假设检验过程。我们的测试方法自动考虑到的依赖结构内的去偏估计，并允许测试组件的数量是指数高。
We propose two semiparametric versions of the debiased Lasso procedure for the model $Y_i = X_i\beta_0 + g_0(Z_i) + \epsilon_i$, where $\beta_0$ is high dimensional but sparse (exactly or approximately). Both versions are shown to have the same asymptotic normal distribution and do not require the minimal signal condition for statistical inference of any component in $\beta_0$. Our method also works when $Z_i$ is high dimensional provided that the function classes $E(X_{ij} |Z_i)$s and $E(Y_i|Z_i)$ belong to exhibit certain sparsity features, e.g., a sparse additive decomposition structure. We further develop a simultaneous hypothesis testing procedure based on multiplier bootstrap. Our testing method automatically takes into account of the dependence structure within the debiased estimates, and allows the number of tested components to be exponentially high.