Related papers: Improving D-Optimality in Nonlinear Situations
We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The…
Optimal experimental design is a well studied field in applied science and engineering. Techniques for estimating such a design are commonly used within the framework of parameter estimation. Nonetheless, in recent years parameter…
In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…
A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the…
Additive models play an essential role in studying non-linear relationships. Despite many recent advances in estimation, there is a lack of methods and theories for inference in high-dimensional additive models, including confidence…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
We propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model. In contrast to the commonly used geometric approach, we use an approach based on algebraic tools. Considerations…
A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…
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 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…
Optimal design theory for nonlinear regression studies local optimality on a given design space. We identify designs for the Bradley--Terry paired comparison model with small undirected graphs and prove that every saturated D-optimal design…
We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
Locally optimal designs for generalized linear models are derived at certain values of the regression parameters. In the present paper a general setup of the generalized linear model is considered. Analytic solutions for optimal designs are…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
Optimal designs can help experimenters obtain more accurate parameter estimates with reduced experimental time and cost. In this paper, we characterize the Expected Weighted (EW) D-optimal designs as robust designs against unknown parameter…
We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$, estimation and inference is…