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(1) > 0 versus K: 1 E RK. We extend these re...

In the context of a pre-existing resource inequality, the concerns for strict equality (allocating the same number of resources to all recipients) conflict with the concerns for equity (allocating resources to rectify the inequality). This study demonstrated age-related changes in children's (3-8 years old, N = 133) ability to simultaneously weigh the concerns for equality and equity through th...

Using an elementary argument we find an upper bound on the Yamabe constant of the outermost minimal hypersurface of an asymptotically flat manifold with nonnegative scalar curvature that satisfies the Riemannian Penrose Inequality. Provided the manifold satisfies the Riemannian Penrose Inequality with rigidity, we show that equality holds in the inequality if and only if the manifold is the Rie...

OBJECTIVE Considering both the economic crisis of 2008 and the Gender Equality Law (2007), this study analyses the association between gender inequality in Spanish Autonomous Communities (AC) and intimate partner violence (IPV) from 2006 to 2014 in terms of socio-demographic characteristics. METHODS Ecological study in the 17 Spanish AC on the correlation between the reported cases by IPV and...

• Pre-Hilbert spaces: definition • Cauchy-Schwarz-Bunyakowski inequality • Example: spaces ` • Triangle inequality, associated metric, continuity issues • Hilbert spaces, completions, infinite sums • Minimum principle • Orthogonal projections to closed subspaces • Orthogonal complements W⊥ • Riesz-Fischer theorem on linear functionals • Orthonormal sets, separability • Parseval equality, Bessel...

The standard proof of the uniform convexity of L using Clarkson’s [1] or Hanner’s [2] inequalities (see also [4]) is rarely taught in functional analysis classes, in part (the author imagines) because the proofs of those inequalities are quite non-intuitive and unwieldy. We present here a direct proof, cheerfully sacrificing the optimal bounds – for which, see [2, 4]. It fits quite nicely in wi...

A self-adaptive fitness formulation is presented for constrained evolutionary optimization. The method has been formulated to ensure that slightly infeasible solutions with a low objective function value remain fit. This is seen as a benefit in solving highly constrained problems that have solutions on one or more of the constraint bounds. In contrast, solutions furthest from the constraint bou...