{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T13:16:27Z","timestamp":1762866987357},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2016,12,5]],"date-time":"2016-12-05T00:00:00Z","timestamp":1480896000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p>We study the properties of the integrated score estimator (ISE), which is the Laplace version of Manski\u2019s maximum score estimator (MMSE). The ISE belongs to a class of estimators whose basic asymptotic properties were studied in Jun, Pinkse, and Wan (2015, <jats:italic>Journal of Econometrics<\/jats:italic> 187(1), 201\u2013216). Here, we establish that the MMSE, or more precisely <jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466616000463_inline1\" \/><jats:tex-math>$$\\root 3 \\of n |\\hat \\theta _M  - \\theta _0 |$$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, (locally first order) stochastically dominates the ISE under the conditions necessary for the MMSE to attain its <jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0266466616000463_inline2\" \/><jats:tex-math>$\\root 3 \\of n $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> convergence rate and that the ISE has the same convergence rate as Horowitz\u2019s smoothed maximum score estimator (SMSE) under somewhat weaker conditions. An implication of the stochastic dominance result is that the confidence intervals of the MMSE are for any given coverage rate wider than those of the ISE, provided that the input parameter \u03b1<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub> is not chosen too large. Further, we introduce an inference procedure that is not only rate adaptive as established in Jun et al. (2015), but also uniform in the choice of \u03b1<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>. We propose three different first order bias elimination procedures and we discuss the choice of input parameters. We develop a computational algorithm for the ISE based on the Gibbs sampler and we examine implementational issues in detail. We argue in favor of normalizing the norm of the parameter vector as opposed to fixing one of the coefficients. Finally, we evaluate the computational efficiency of the ISE and the performance of the ISE and the proposed inference procedure in an extensive Monte Carlo study.<\/jats:p>","DOI":"10.1017\/s0266466616000463","type":"journal-article","created":{"date-parts":[[2016,12,5]],"date-time":"2016-12-05T10:29:20Z","timestamp":1480933760000},"page":"1418-1456","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":3,"title":["INTEGRATED SCORE ESTIMATION"],"prefix":"10.1017","volume":"33","author":[{"given":"Sung Jae","family":"Jun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joris","family":"Pinkse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanyuan","family":"Wan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,12,5]]},"reference":[{"key":"S0266466616000463_ref15","doi-asserted-by":"crossref","first-page":"387","DOI":"10.2307\/2951556","article-title":"An efficient semiparametric estimator for binary response models","volume":"61","author":"Klein","year":"1993","journal-title":"Econometrica"},{"key":"S0266466616000463_ref24","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1145\/377939.377946","article-title":"A note on a method for generating points uniformly on n-dimensional spheres","volume":"2","author":"M\u00fcller","year":"1959","journal-title":"Communications of the ACM"},{"key":"S0266466616000463_ref23","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2307\/1913240","article-title":"Semiparametric analysis of random effects linear models from binary panel data","volume":"55","author":"Manski","year":"1987","journal-title":"Econometrica"},{"key":"S0266466616000463_ref30","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.2307\/1913713","article-title":"Semiparametric estimation of index coefficients","volume":"57","author":"Powell","year":"1989","journal-title":"Econometrica"},{"key":"S0266466616000463_ref21","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0304-4076(75)90032-9","article-title":"Maximum score estimation of the stochastic utility model of choice","volume":"3","author":"Manski","year":"1975","journal-title":"Journal of Econometrics"},{"key":"S0266466616000463_ref31","volume-title":"Approximate Calculation of Multiple Integrals","author":"Stroud","year":"1971"},{"key":"S0266466616000463_ref27","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1017\/S0266466600012408","article-title":"Partially identified econometric models","volume":"5","author":"Phillips","year":"1989","journal-title":"Econometric Theory"},{"key":"S0266466616000463_ref32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2545-2","volume-title":"Weak Convergence and Empirical Processes","author":"van der Vaart","year":"1996"},{"key":"S0266466616000463_ref28","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0304-4076(93)90118-O","article-title":"On the computation of semiparametric estimates in limited dependent variable models","volume":"58","author":"Pinkse","year":"1993","journal-title":"Journal of Econometrics"},{"key":"S0266466616000463_ref25","unstructured":"Patra, R.K. , Seijo, E. , & Sen, B. 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