TY - JOUR
AU - 
AB - <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>(β) ≥ 0 versus <jats:italic>K</jats:italic>: β ∈ <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>(β) ≥ 0 and <jats:italic>h</jats:italic><jats:sub>2</jats:sub>(β) = 0 versus <jats:italic>K</jats:italic>: β ∈ <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 χ<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>
TI - Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models
JF - Econometric Theory
DO - 10.1017/s0266466600012238
DA - 1989-04-01
UR - https://www.deepdyve.com/lp/crossref/local-and-global-testing-of-linear-and-nonlinear-inequality-okEi0MDSFV
SP - 1
EP - 35
VL - 5
IS - 1
DP - DeepDyve
ER -