{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T12:26:15Z","timestamp":1791635175038,"version":"4.3.4"},"reference-count":44,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T00:00:00Z","timestamp":1287360000000},"content-version":"unspecified","delay-in-days":7870,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[1989,4]]},"abstract":"<jats:p>This paper considers a general nonlinear econometric model framework that contains a large class of estimators defined as solutions to optimization problems. For this framework we derive several asymptotically equivalent forms of a test statistic for the local (in a way made precise in the paper) multivariate nonlinear inequality constraints test<jats:italic>H<\/jats:italic>:<jats:italic>h<\/jats:italic>(\u03b2) \u2265 0 versus<jats:italic>K<\/jats:italic>: \u03b2 \u2208<jats:italic>R<jats:sup>K<\/jats:sup><\/jats:italic>. We extend these results to consider local hypotheses tests of the form<jats:italic>H<\/jats:italic>:<jats:italic>h<\/jats:italic><jats:sub>1<\/jats:sub>(\u03b2) \u2265 0 and<jats:italic>h<\/jats:italic><jats:sub>2<\/jats:sub>(\u03b2) = 0 versus<jats:italic>K<\/jats:italic>: \u03b2 \u2208<jats:italic>R<jats:sup>K<\/jats:sup><\/jats:italic>. For each test we derive the asymptotic distribution for any size test as a weighted sum of \u03c7<jats:sup>2<\/jats:sup>-distributions. We contrast local as opposed to global inequality constraints testing and give conditions on the model and constraints when each is possible. This paper also extends the well-known duality results in testing multivariate equality constraints to the case of nonlinear multivariate inequality constraints and combinations of nonlinear inequality and equality constraints.<\/jats:p>","DOI":"10.1017\/s0266466600012238","type":"journal-article","created":{"date-parts":[[2010,10,18]],"date-time":"2010-10-18T09:11:55Z","timestamp":1287393115000},"page":"1-35","source":"Crossref","is-referenced-by-count":72,"title":["Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models"],"prefix":"10.1017","volume":"5","author":[{"given":"Frank 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