Related papers: D-optimal Designs for Multinomial Logistic Models
Simulation-based optimal design techniques are a convenient tool for solving a particular class of optimal design problems. The goal is to find the optimal configuration of factor settings with respect to an expected utility criterion. This…
Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with uncertainties…
This work proposes multi-agent systems setting for concurrent engineering system design optimization and gradually paves the way towards examining graph theoretic constructs in the context of multidisciplinary design optimization problem.…
In this paper, we derive optimal designs for the Rasch Poisson counts model and the Rasch Poisson-Gamma counts model incorporating several binary predictors for the difficulty parameter. To efficiently estimate the regression coefficients…
The paper derives new results on the marginal likelihood of a two-way table which clarify the conditions under which Ecological inference is possible and lead to an efficient algorithm for maximizing the exact multinomial likelihood. The…
In discrete choice experiments, the information matrix depends on the model parameters. Therefore designing optimally informative experiments for arbitrary initial parameters often yields highly nonlinear optimization problems and makes…
It is often desired that ordinal regression models yield unimodal predictions. However, in many recent works this characteristic is either absent, or implemented using soft targets, which do not guarantee unimodal outputs at inference. In…
This article will devise data-driven, mathematical laws that generate optimal, statistical classification systems which achieve minimum error rates for data distributions with unchanging statistics. Thereby, I will design learning machines…
Optimal designs for generalized linear models require a prior knowledge of the regression parameters. At certain values of the parameters we propose particular assumptions which allow to derive a locally optimal design for a model without…
Let the design of an experiment be represented by an $s$-dimensional vector $\mathbf {w}$ of weights with nonnegative components. Let the quality of $\mathbf {w}$ for the estimation of the parameters of the statistical model be measured by…
We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular $T$-optimality criterion are derived, which in many…
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 present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
In this paper we consider the problem of constructing $T$-optimal discriminating designs for Fourier regression models. We provide explicit solutions of the optimal design problem for discriminating between two Fourier regression models,…
In this paper we construct (locally) $D$-optimal designs for a wide class of non-linear multiple regression models, when the design region is a $k$-dimensional ball. For this construction we make use of the concept of invariance and…
One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods,…
We consider an assortment optimization problem under the multinomial logit choice model with general covering constraints. In this problem, the seller offers an assortment that should contain a minimum number of products from multiple…
The experimental design for a generalized linear model (GLM) is important but challenging since the design criterion often depends on model specification including the link function, the linear predictor, and the unknown regression…
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…
This article introduces an iterative distributed computing estimator for the multinomial logistic regression model with large choice sets. Compared to the maximum likelihood estimator, the proposed iterative distributed estimator achieves…