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We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than-<jats:italic>n<\/jats:italic>bootstrap to making inferences on these bounds. The finite sample performances of the confidence intervals for the bounds based on normal critical values, the standard bootstrap, and the fewer-than-<jats:italic>n<\/jats:italic>bootstrap are investigated via a simulation study. Finally we establish sharp bounds on the treatment effect distribution when covariates are available.<\/jats:p>","DOI":"10.1017\/s0266466609990168","type":"journal-article","created":{"date-parts":[[2009,10,7]],"date-time":"2009-10-07T09:26:28Z","timestamp":1254907588000},"page":"931-951","source":"Crossref","is-referenced-by-count":91,"title":["SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE"],"prefix":"10.1017","volume":"26","author":[{"given":"Yanqin","family":"Fan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sang Soo","family":"Park","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2009,10,7]]},"reference":[{"key":"S0266466609990168_ref67","doi-asserted-by":"publisher","DOI":"10.1016\/0888-613X(90)90022-T"},{"key":"S0266466609990168_ref64","doi-asserted-by":"publisher","DOI":"10.2307\/2297326"},{"key":"S0266466609990168_ref63","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994668"},{"key":"S0266466609990168_ref61","first-page":"229","article-title":"Fonctions de r\u00e9artition \u00e0 n dimensions et leures marges","volume":"8","author":"Sklar","year":"1959","journal-title":"Publications de l'Institut de Statistique de L'Universit\u00e9 de Paris"},{"key":"S0266466609990168_ref60","doi-asserted-by":"crossref","unstructured":"Shaikh A.M. & Vytlacil E. 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