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非线性模型中涉及不等式约束的假设检验的局部性质AI 解读

This paper derives several properties unique to nonlinear model hypothesis testing problems involving linear or nonlinear inequality constraints in the null or alternative hypothesis. The paper is organized around a lemma that characterizes the set containing the least favorable parameter value for a nonlinear model inequality constraints hypothesis test. The author then presents two examples that illustrate several implications of this lemma. He also discusses the impact of…

线性计量模型中的不等式约束检验AI 解读

This paper develops three asymptotically equivalent tests for examining the validity of imposing linear inequality restrictions on the parameters of linear econometric models. First we consider the model y = Xβ + ε, where ε is N(0, Σ), and the hypothesis test H: Rβ≥r versus K: β ϵ RK. Later we generalize this testing framework to the linear simultaneous equations model. We show that the joint asymptotic distribution of these test statistics and the test statistics from the…

非线性计量模型中线性与非线性不等式约束的局部和全局检验AI 解读

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…

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多元假设检验中的对偶性AI 解读

This paper derives a duality result for a general class of hypothesis testing problems in multivariate analysis utilizing the relationship between convex cones and their polar cones together with the properties of minimum norm problems between points and cones in Euclidian space. Special cases of this result yield generalizations of a well-known duality relation in multivariate equality constraints testing. For example, any multivariate inequality constraints test on the…

线性回归中多重不等式与等式约束的精确检验AI 解读

In this article we consider the linear regression model y = Xβ + ε, where ε is N(0, σ2I). In this context we derive exact tests of the form H: Rβ ≥ r versus K: β ∈ RK for the case in which θ2 is unknown. We extend these results to consider hypothesis tests of the form H: R1β ≥ r1 and R2β = r2 versus K: (β ∈ RK . For each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming. For both tests we…