Related papers: $T$-optimal designs for discrimination between two…

Tight $2 s$-designs are the $2 s$-$(v, k, \lambda)$ designs whose sizes achieve the Fisher type lower bound ${v \choose s}$. Symmetric $2$-designs, the Witt $4$-$(23, 7, 1)$ design and the Witt $4$-$(23, 16, 52)$ design are tight designs.…

In both Tweedie and geometric Tweedie models, the common power parameter $p\notin(0,1)$ works as an automatic distribution selection. It mainly separates two subclasses of semicontinuous ($1<p<2$) and positive continuous ($p\geq 2$)…

Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…

In a recent paper Dette et al. (2014) introduced optimal design problems for dose fnding studies with an active control. These authors concentrated on regression models with normal distributed errors (with known variance) and the problem of…

We study T-semidefinite programming (SDP) relaxation for constrained polynomial optimization problems (POPs). T-SDP relaxation for unconstrained POPs was introduced by Zheng, Huang and Hu in 2022. In this work, we propose a T-SDP relaxation…

In this paper we elucidate the advantage of examining the connections between Hilbert-Kamke equations and geometric designs, or Chebyshev-type quadrature, for classical orthogonal polynomials. We first establish that if a $5$-design with…

We consider optimal designs for general multinomial logistic models, which cover baseline-category, cumulative, adjacent-categories, and continuation-ratio logit models, with proportional odds, non-proportional odds, or partial proportional…

We show that the problem of finding the measure supported on a compact subset K of the complex plane such that the variance of the least squares predictor by polynomials of degree at most n at a point exterior to K is a minimum, is…

Many existing methods for constructing optimal split-plot designs, such as D-optimal designs, only focus on minimizing the variances and covariances of the estimation for the fitted model. However, the underlying true model is usually…

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…

We develop $D$-optimal designs for linear main effects models on a subset of the $2^K$ full factorial design region, when the number of factors set to the higher level is bounded. It turns out that in the case of narrow margins only those…

This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…

Let $\mathrm{R}$ be a real closed field. The problem of obtaining tight bounds on the Betti numbers of semi-algebraic subsets of $\mathrm{R}^k$ in terms of the number and degrees of the defining polynomials has been an important problem in…

There is a movement in design of experiments away from the classic randomization put forward by Fisher, Cochran and others to one based on optimization. In fixed-sample trials comparing two groups, measurements of subjects are known in…

In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and…

The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…

We describe an algorithm which finds binomials in a given ideal $I\subset\mathbb{Q}[x_1,\dots,x_n]$ and in particular decides whether binomials exist in $I$ at all. Binomials in polynomial ideals can be well hidden. For example, the lowest…

Let $n\in\mathbb{N}$ be fixed, $Q>1$ be a real parameter and $\mathcal{P}_n(Q)$ denote the set of polynomials over $\mathbb{Z}$ of degree $n$ and height at most $Q$. In this paper we investigate the following counting problems regarding…

We study a Markov decision problem in which the state space is the set of finite marked point configurations in the plane, the actions represent thinnings, the reward is proportional to the mark sum which is discounted over time, and the…

In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A necessary condition for the optimality of a given design is…