A polynomial functional relationship with errors in both variables can be consistently estimated by constructing an ordinary least squares estimator for the regression coef®cients, assuming hypothetically the latent true regressor variable to be known, and then adjusting for the errors. If normality of the error variables can be assumed, the estimator can be simpli®ed considerably. Only the variance of the errors in the regressor variable and its covariance with the errors of the response variable need to be known. If the variance of the errors in the dependent variable is also known, another estimator can be constructed.

Polynomial regression models with errors in variables are considered. A goodness-of-fit test is constructed, which is based on an adjusted least-squares estimator and modifies the test introduced by Zhu et al. for a linear structural model with normal distributions. In the present paper, the distributions of errors are not necessarily normal. The proposed test is based on residuals, and it is asymptotically chi-squared under null hypothesis. We discuss the power of the test and the choice of an exponent in the exponential weight function involved in test statistics.

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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].