Related papers: Complete classes of designs for nonlinear regressi…

For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev…

In this paper, we establish a priori estimates for a class of fully nonlinear equations with Neumann boundary conditions. By the continuity method, we have obtained the existence theorem for the Neumann problem.

We establish cartesian model structures for variants of $\Theta_n$-spaces in which we replace some or all of the completeness conditions by discreteness conditions. We prove that they are all equivalent to each other and to the…

The celebrated de la Garza phenomenon states that for a polynomial regression model of degree $p-1$ any optimal design can be based on at most $p$ design points. In a remarkable paper, Yang [Ann. Statist. 38 (2010) 2499--2524] showed that…

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…

We propose a well-posed Maxwell-type boundary condition for the linear moment system in half-space. As a reduction of the Boltzmann equation, the moment equations are available to model Knudsen layers near a solid wall, where proper…

In a seminal paper \cite{studden1968} characterized $c$-optimal designs in regression models, where the regression functions form a Chebyshev system. He used these results to determine the optimal design for estimating the individual…

Sloppy models are complex nonlinear models with outcomes that are significantly affected by only a small subset of parameter combinations. Despite forming an important universality class and arising frequently in practice, formal and…

We extend the approach in [Ann. Statist. 38 (2010) 2499-2524] for identifying locally optimal designs for nonlinear models. Conceptually the extension is relatively simple, but the consequences in terms of applications are profound. As we…

We consider maximin and Bayesian $D$-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes…

The new formulation of the causal completion of spacetimes suggested in [1], and modified later in [2], is tested by computing the causal boundary for product spacetimes of a Lorentz interval and a Riemannian manifold. This is…

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…

We consider a general class of non-linear Bellman equations. These open up a design space of algorithms that have interesting properties, which has two potential advantages. First, we can perhaps better model natural phenomena. For…

Statistical latent class models are widely used in social and psychological researches, yet it is often difficult to establish the identifiability of the model parameters. In this paper we consider the identifiability issue of a family of…

Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is…

This paper studies point identification of the distribution of the coefficients in some random coefficients models with exogenous regressors when their support is a proper subset, possibly discrete but countable. We exhibit trade-offs…

This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…

Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…

We prove estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. These equations are not arbitrary, but arise naturally in the study of conformal geometry.

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [1991, A log-linear…