7 Constraint generation and quadratic inequalities 29 7.1 Example: the stable set polytope again . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.2 Strong insolvability of quadratic equations . . . . . . . . . . . . . . . . . . . . . . . . 30 7.3 Inference rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 7.4 Algorithmic aspects of inference rules . ...

7 Constraint generation and quadratic inequalities 29 7.1 Example: the stable set polytope again . . . . . . . . . . . . . . . . . . . . . . . . . . 29 7.2 Strong insolvability of quadratic equations . . . . . . . . . . . . . . . . . . . . . . . . 30 7.3 Inference rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 7.4 Algorithmic aspects of inference rules . ...

Inference methods for the positive stable laws, which have no closed form expression for the density functions are developed based on a special quadratic distance using negative moments. Asymptotic properties of the quadratic distance estimator (QDE) are established. The QDE is shown to have asymptotic relative efficiency close to 1 for almost all the values of the parameter space. Goodness-of-...

The estimation of quadratic functions of a multivariate normal mean is an inferential problem which, while being simple to state and often encountered in practice, leads to surprising complications both from frequentist and Bayesian points of view. The drawbacks of Bayesian inference using the constant noninformative prior are now well established and we consider in this paper the advantages an...

water quality prediction is a valuable tool for pollutant control in aquatic environments. a river system is selected and one-dimensional flow is assumed for the simulation of pollutant transport in this paper. advective and diffusive terms of transport equation are considered separately. different functions of advective transport are proposed and applied for a specified velocity on the discret...

Hansen (1982) proposed the generalised method of moments (GMMs) for estimating a vector of regression parameters from a set of score functions. Hansen established that, under certain regularity conditions, the GMMs estimator is consistent, asymptotically normal, and asymptotically efficient. In the generalised estimating equation framework, Qu, Lindsay & Li (2000) extended the GMMs to create a ...

Popular methods for estimating the central subspace in regression require slicing a continuous response. However, slicing can result in loss of information and in some cases that loss can be substantial. We use intraslice covariances to construct improved inference methods for the central subspace. These methods are optimal within a class of quadratic inference functions and permit chi-squared ...

Exponential Random Graphs Models (ERGM) are common, simple statistical models for social network and other network structures. Unfortunately, inference and learning with them is hard even for small networks because their partition functions are intractable for precise computation. In this paper, we introduce a new quadratic time deterministic approximation to these partition functions. Our main...