{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:38:37Z","timestamp":1760243917769,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2010,6,14]],"date-time":"2010-06-14T00:00:00Z","timestamp":1276473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper develops a semi-parametric, Information-Theoretic method for estimating parameters for nonlinear data generated under a sample selection process. Considering the sample selection as a set of inequalities makes this model inherently nonlinear. This estimator (i) allows for a whole class of different priors, and (ii) is constructed as an unconstrained, concentrated model. This estimator is easy to apply and works well with small or complex data. We provide a number of explicit analytical examples for different priors\u2019 structures and an empirical example.<\/jats:p>","DOI":"10.3390\/e12061569","type":"journal-article","created":{"date-parts":[[2010,6,14]],"date-time":"2010-06-14T11:40:21Z","timestamp":1276515621000},"page":"1569-1580","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Concentrated, Nonlinear Information-Theoretic Estimator for the Sample Selection Model"],"prefix":"10.3390","volume":"12","author":[{"given":"Amos","family":"Golan","sequence":"first","affiliation":[{"name":"Department of Economics and the Info-Metrics Institute, American University, Kreeger Hall 104, 4400 Massachusetts Ave., NW, Washington, DC 20016-8029, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henryk","family":"Gzyl","sequence":"additional","affiliation":[{"name":"Centro de Finanzas, IESA, Caracas, Venezuela"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2010,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"153","DOI":"10.2307\/1912352","article-title":"Sample selection bias as a specification error","volume":"47","author":"Heckman","year":"1979","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0304-4076(85)90009-0","article-title":"Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator","volume":"27","author":"Manski","year":"1985","journal-title":"J. Econom."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"765","DOI":"10.2307\/1912157","article-title":"Distribution-free maximum likelihood estimator of the binary choice model","volume":"51","author":"Cosslett","year":"1981","journal-title":"Econometrica"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0304-4076(87)90030-3","article-title":"Non-parametric analysis of a generalized regression model: The maximum rank correlation estimator","volume":"35","author":"Han","year":"1987","journal-title":"J. Econom."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0304-4076(93)90111-H","article-title":"Semiparametric estimation of censored selection models with a nonparametric selection mechanism","volume":"58","author":"Ahn","year":"1993","journal-title":"J. Econom."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1081\/ETC-120028837","article-title":"A small sample estimation of the sample selection model","volume":"23","author":"Golan","year":"2004","journal-title":"Econom. Rev."},{"key":"ref_7","unstructured":"Golan, A., Judge, G., and Miller, D. (1996). Maximum Entropy Econometrics: Robust Estimation with Limited Data, John Wiley & Sons."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/S0304-4076(97)00006-7","article-title":"Recovering information from censored and ordered multinomial response data","volume":"79","author":"Golan","year":"1997","journal-title":"J. Econom."},{"key":"ref_9","first-page":"2","article-title":"An information theoretic approach for estimating nonlinear dynamic models","volume":"7","author":"Golan","year":"2003","journal-title":"Nonlinear Dynamics Econom."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Maddala, G.S. (1983). Limited-Dependent and Qualitative Variables in Econometrics, Cambridge University Press.","DOI":"10.1017\/CBO9780511810176"},{"key":"ref_11","unstructured":"Kullback, S. (1959). Information Theory and Statistics, John Wiley & Sons."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Statist."},{"key":"ref_13","unstructured":"Gokhale, D.V., and Kullback, S. (1978). The Information in Contingency Tables, Marcel Dekker."},{"key":"ref_14","unstructured":"Golan, A., and Gzyl, H. (2008). An information theoretic estimator for the linear model. Working paper."},{"key":"ref_15","unstructured":"Due to the small size of the data and the large proportion of censored observations, none of the maximum likelihood methods would converge with all standard software."},{"key":"ref_16","unstructured":"For discussion of the data, detailed analyses and discussion of the different estimators as well as a detailed discussion of the AP [5] application, see GMP [6]. The 2-step and AP estimates are taken from that paper, Table 8."},{"key":"ref_17","unstructured":"To keep the Table simple and since these specific results are not of interested here, they are not presented."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/6\/1569\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:02:41Z","timestamp":1760220161000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/12\/6\/1569"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,14]]},"references-count":17,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2010,6]]}},"alternative-id":["e12061569"],"URL":"https:\/\/doi.org\/10.3390\/e12061569","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2010,6,14]]}}}