causal_statのノート

R, Tex, データサイエンスに関するノート

Synthetic Control Method (SCM)

Causal inference

論文

SCM はパネルデータを用いてATT (処置群における平均処置効果)を推定する方法である。
コントロールユニットの系列ベクトルたちの１次結合より合成コントロールを構成する。

  • The Economic Costs of Conflict: A Case Study of the Basque Country. Abadie, Gardeazabal. AMERICAN ECONOMIC REVIEW, VOL. 93, NO. 1, MARCH 2003, pp. 113-132.
  • Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program. Abadie, Diamond and Hainmueller
  • Comparative Politics and the Synthetic Control Method. Abadie, Diamond and Hainmueller. American Journal of Political Science, Vol. 59, No. 2, April 2015, Pp. 495–510.
  • Xu, Yiqing, 2017. “Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models.” Political Analysis, Volume 25, Issue 1, January 2017, pp. 57-76.
  • Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis. Nikolay Doudchenko, Guido W. Imbens
  • Athey, Bayati, Doudchenko, Imbens, Khosravi (2018). Matrix Completion Methods for Causal Panel Data Models


R package

https://cran.r-project.org/web/packages/Synth/Synth.pdf

Synth: An R Package for Synthetic Control Methods in Comparative Case Studies
Abadie, Diamond, Hainmueller

LASSO リソース

Machine learning

LASSO リソース

Hastie, Tibshirani and Wainwright,
Statistical Learning with Sparsity: The Lasso and Generalizations
SLSと省略する

LASSOの計算方法
Coordinate descent, SLS, p15

Elastic Net, SLS chapter 4

Fused Lasso, SLS

Group Lasso

Adaptive Lasso

関数データ解析, 川野、松井、廣瀬, chap 3

Papers on CV

Statistics Machine learning

Survey

  • Sylvain Arlot and Alain Celisse (2010).

A survey of cross-validation procedures for model selection
Statist. Surv.Volume 4 (2010), 40-79.


Regression

  • L. Breiman and P. Spector (1992). Submodel selection and evaluation in regression. The X-random case. International Statistical Review. pp. 291-319.
  • M. Stone (1974). Cross-Validatory Choice and Assessment of Statistical Predictions. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 36, No. 2, pp. 111-147,
  • J. Shao and Tu. The jacknife and bootstrap. Chapter 7.
  • J. Shao (1993). Linear Model Selection by Cross-Validation.

Journal of the American Statistical Association, Vol. 88, No. 422 (Jun., 1993), pp. 486-494

v-fold cross-validation

  • Prabir Burman (1989). A Comparative Study of Ordinary Cross-Validation, v-Fold Cross-Validation and the Repeated Learning-Testing Methods. Biometrika, Vol. 76, No. 3 (Sep., 1989), pp. 503-514

Density estimation

  • Alain Celisse (2014). Optimal cross-validation in density estimation with the L2-loss

Ann. Statist., Volume 42, Number 5 (2014), 1879-1910.
(Theoretical investigation of Lpo CV.)

Classification

  • A. Cellise and Tristan Mary-Huard (2018).

Theoretical Analysis of Cross-Validation for Estimating the Risk of the k-Nearest Neighbor Classifier. Journal of Machine Learning Research 18 (2018) 1-54



Dependent data

  • Prabir Burman, EDMOND CHOW and Deborah Nolan (1994).

A Cross-Validatory Method for Dependent Data. Biometrika 81(2):351-358

  • Jack Racine (2000). Consistent cross-validatory model-selection

for dependent data: hv-block cross-validation.
Journal of Econometrics 99 (2000) 39}61

Papers on U-statistics

List of papers on U-statistics by subjects

Fundamental

  • Wassily Hoeffding (1948). A Class of Statistics with Asymptotically Normal Distribution

Ann. Math. Statist., Volume 19, Number 3 (1948), 293-325.

Strong law

  • W Hoeffding (1961). The strong law of large numbers for u-statistics. North Carolina State University. Dept. of Statistics.
  • Tasos C. Christofides (1992). A strong law of large numbers for U-statistics. Journal of Statistical Planning and Inference. Volume 31, Issue 2, May 1992, Pages 133-145

Asymptotic Normality

Asymptotic Normality of studentized U-statistics

  • Bing-Yi Jing, Qiying Wang, and Lincheng Zhao (2000). The Berry-Esséen bound for Studentized statistics

Ann. Probab. Volume 28, Number 1 (2000), 511-535.

  • Qi-Man Shao, Kan Zhang, Wen-Xin Zhou (2015).

Stein’s method for nonlinear statistics: A brief survey and recent progress
Journal of Statistical Planning and Inference 168

Statistical inference

  • Hien D. Nguyen (2019). Concentration-based confidence intervals for U-statistics, ArXiv.

U-statistics with increasing degree

  • Edward W. Frees (1989). Infinite Order U-Statistics. Scandinavian Journal of Statistics

Vol. 16, No. 1 (1989), pp. 29-45.

  • Charles Heilig and Deborah Nolan (2001). Limit theorems for the infinite-degree U-process.

Statistica Sinica. Vol. 11, No. 1 (January 2001), pp. 289-302

  • Grzegorz A Rempala and Arjun Gupta (1999). Weak limits of U -statistics of infinite order.

Random Operators and Stochastic Equations 7(1):39-52

Berry-Esseen type bound

  • Louis H.Y. Chen and Qi-Man Shao (2007). Normal approximation for nonlinear statistics using a concentration inequality approach. Bernoulli, Volume 13, Number 2 (2007), 581-599.

Jackknife estimator of variance

  • James N. Arvesen (1969). Jackknifing U-Statistics. The Annals of Mathematical Statistics

Vol. 40, No. 6 (Dec., 1969), pp. 2076-2100


Incomplete U-statistics