{"title":"Testing for the presence of treatment effect under selection on observables","authors":"Pier Luigi Conti, Livia De Giovanni","doi":"10.1007/s10182-022-00454-8","DOIUrl":null,"url":null,"abstract":"<div><p>The evaluation of the possible effects of a treatment on an outcome plays a central role in both theoretical and applied statistical and econometrical literature. This paper focuses on nonparametric tests for possible difference in the distribution of potential outcomes due to receiving or not receiving a treatment. The approach is based on weighting observed data on the basis on the estimated propensity score. Kolmogorov–Smirnov type and Wilcoxon–Mann–Whitney type tests are constructed, and their limiting distributions are studied. Rejection regions are obtained by inverting confidence intervals. This involves the study of appropriate estimators of the limiting variance of test statistics. Approximations of quantiles <i>via</i> subsampling are also considered. The merits of the different tests are studied by Monte Carlo simulation. An application to the construction of tests for stochastic dominance is provided.</p></div>","PeriodicalId":55446,"journal":{"name":"Asta-Advances in Statistical Analysis","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2022-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10182-022-00454-8.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asta-Advances in Statistical Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10182-022-00454-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
The evaluation of the possible effects of a treatment on an outcome plays a central role in both theoretical and applied statistical and econometrical literature. This paper focuses on nonparametric tests for possible difference in the distribution of potential outcomes due to receiving or not receiving a treatment. The approach is based on weighting observed data on the basis on the estimated propensity score. Kolmogorov–Smirnov type and Wilcoxon–Mann–Whitney type tests are constructed, and their limiting distributions are studied. Rejection regions are obtained by inverting confidence intervals. This involves the study of appropriate estimators of the limiting variance of test statistics. Approximations of quantiles via subsampling are also considered. The merits of the different tests are studied by Monte Carlo simulation. An application to the construction of tests for stochastic dominance is provided.
期刊介绍：
AStA - Advances in Statistical Analysis, a journal of the German Statistical Society, is published quarterly and presents original contributions on statistical methods and applications and review articles.
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