Chung and Romano (2013) Exact and Asymptotically Robust Permutation Tests, AOS.

Introduction IID. IID. とは independent. Let and write \begin{align*}Z = (Z_1, \ldots, Z_N) = (X_1, \ldots, X_m, Y_1, \ldots, Y_n)\end{align*} . であるとき，の同時分布は任意のの分布に等しい。ただし，はの permutation. をすべての permut…

2021-02-23

Aronow, Samii & Wang (2020) Design-based inference for spatial experiments with interference, arXiv.

Causal Inference on Spatial Data Design-Based Uncertainty Survey

Setting intervention points: . Each point resides in (lattitude and longitude). An experimental design assigns a treatment to each intervention point. . Design-based inference = のみランダム，他の変数はすべて固定値． : potential outcome at…

2021-02-21

Hong, Leung & Li (2020) Inference on finite-population treatment effects under limited overlap, Econometrics J.

Design-Based Uncertainty Survey

Average Treatment Effect observed units, : treatment assignment, : potential outcome under , and : vector of baseline covariates. 以外は全て固定の個人属性とする．観測データ: , where . Stratum of = , where は有限集合． Conditionally indepe…

2021-02-19

Abadie, Athey, Imbens & Wooldridge (2020) Sampling-based versus design-based uncertainty in regression analysis, ECTA.

Design-Based Uncertainty Survey

Section 1. Introduction Sampling-based uncertainty: パラメータ推定のランダムネスは母集団からのランダムなサンプリングによるものと考える．母集団が（無限に）大きいときにはこの考え方は妥当．しかし，母集団として州や国を観測単位とするときには不…

2021-02-16

Rambachan and Roth (2020) Design-based uncertainty for quasi-experiments, arXiv.

Design-Based Uncertainty Survey

Section 2: A finite population model for quasi-experiments サイズの有限母集団を考える*1． Binary treatment: , potential outcomes: . Potential outcome は固定値と仮定する． Observed outcome: . 各が独立にトリートメントを受ける確率をとする…