A goodness-of-fit test for a polynomial errors-in-variables model

Abstract

We establish conditions for the maximal dissipativity of one class of densely-defined closed linear operators in a Hilbert space. The results obtained are applied to the investigation of some special differential boundary operators. This paper is a continuation of [1]; we therefore use the notation and terminology introduced therein. Prior to the formulation of the results, we recall that a linear operator T :, and it is called maximally dissipative (maximally accumulative) if, in addition, it does not have nontrivial dissipative (accumulative) extensions in H. Dissipative operators naturally arise in the investigation of the well-posedness of certain classes of boundaryvalue problems for parabolic and hyperbolic systems of partial differential equations [2,3]. In this case, there often arises the problem of the description of maximally dissipative extensions of a symmetric operator, which has been considered in numerous papers (see, e.g., [4 -7]). We consider a more general problem, namely the problem of conditions for the maximal dissipativity (in particular, self-adjointness) of an almost bounded perturbation of a smooth restriction of an operator adjoint to a symmetric one in the sense of definitions proposed in [8, p. 167].

An Adaptive-to-Model Test for Parametric Single-Index Errors-in-Variables Models

“…A score-type lack-of-fitness test was proposed based on this fact. This testing procedure has been extended to polynomial EIVs models by Cheng and Kukush (2004) and Zhu, Song and Cui (2003) independently, without the normality restriction on the covariates. Hall and Ma (2007) proposed a test based on deconvolution methods assuming that the distribution of the covariate errors is known.…”