The issue of the non-invariance of the Wald test under nonlinear reparametrisations of the restrictions under test is studied from a differential geometric viewpoint. Quantities that can be defined in purely geometrical terms are by construction invariant under reparametrisation, and various...

This paper suggests the use of simple minimum distance methods to estimate restricted cointegrating vectors. The method directly employs minimum distance methods on unrestricted cointegrating matrices estimated in the usual way to estimate restricted parameters which are linearly or nonlinearly...

We consider two Riemannian geometries for the manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathcal{M }(p,m\times n)}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="script">M</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mo>×</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> of all <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m\times n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>m</mi> <mo>×</mo> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation> matrices of rank <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation>. The geometries are induced on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$${\mathcal{M }(p,m\times n)}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="script">M</mi> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>m</mi> <mo>×</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> by viewing it as the base...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The paper treats the issue of prediction in the economic (social) field, in a theoretical framework that replaces the truth with the reasonability. In this end, some already accepted parameters around the prediction need reconfiguration: causality to be replaced with explanatory protocol,...

Space-time manifold plays an important role to express the concepts of Relativity properly. Causality and space-time topology make easier the geometrical explanation of Minkowski space-time manifold. The Minkowski metric is the simplest empty space-time manifold in General Relativity, and is in...

We show that the asymptotic mean of the log-likelihood ratio in a misspecified model is a differential geometric quantity that is related to the exponential curvature of Efron (1978), Amari (1982), and the preferred point geometry of Critchley et al. (1993, 1994). The mean is invariant with...

This paper deals with further developments of the new theory that applies stochastic differential geometry (SDG) to dynamics of interest rates. We examine mathematical constraints on the evolution of interest rate volatilities that arise from stochastic differential calculus under assumptions of...

The partial (ceteris paribus) effects of interest in nonlinear and interactive linear models are heterogeneous as they can vary dramatically with the underlying observed or unobserved covariates. Despite the apparent importance of heterogeneity, a common practice in modern empirical work is to...