Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models
针对一大类由优化问题定义的估计量，推导了局部与全局非线性不等式约束检验的渐近等价统计量及其分布，并扩展至混合等式与不等式约束的检验。
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 H : h (β) ≥ 0 versus K : β ∈ R K . We extend these results to consider local hypotheses tests of the form H : h 1 (β) ≥ 0 and h 2 (β) = 0 versus K : β ∈ R K . For each test we derive the asymptotic distribution for any size test as a weighted sum of χ 2 -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.