Khái niệm cốt lõi
Nonparametric estimation of instrumental variable (IV) regressions with model selection.
Tóm tắt
この論文では、非パラメトリックな楽器変数(IV)回帰の推定に焦点を当て、モデル選択を行います。提案されたRegularized DeepIV(RDIV)アルゴリズムは、Tikhonov正則化を使用して最小二乗解に収束し、モデル選択手法を可能にします。これにより、従来の方法と比較して理論的保証が得られます。
Thống kê
E[Y − h(X)|Z] = 0.
T f = r0 where T : L2(X) ∋ f(X) 7→ E[f(X)|Z] ∈ L2(Z)
δn = max{δn,G, δn,H}
∥ˆh − h0∥2 = O(δ2/α + αmin(β,2))
∥ˆh − h0∥2 = O(δ2/α + αmin(β+1,2)/α)
Trích dẫn
"Our method consists of two stages: first, we learn the conditional distribution of covariates, and by utilizing the learned distribution, we learn the estimator by minimizing a Tikhonov-regularized loss function."
"We propose a two-stage method, the Regularized Deep Instrumental Variable (RDIV), which is summarized in Algorithm 1."
"Our results for the iterative estimator match the state-of-the-art convergence rate with respect to L2 norm for an iterative estimator in Bennett et al. (2023b)."