Optimal designs for nonlinear regression models with respect to non-informative priors

In nonlinear regression models the Fisher information depends on the parameters of the model. Consequently, optimal designs maximizing some functional of the information matrix cannot be implemented directly but require some preliminary knowledge about the unknown parameters. Bayesian optimality criteria provide an attractive solution to this problem. These criteria depend sensitively on a reasonable specification of a prior distribution for the model parameters which might not be available in all applications. In this paper we investigate Bayesian optimality criteria with non-informative prior dis- tributions. In particular, we study the Jeffreys and the Berger-Bernardo prior for which the corresponding optimality criteria are not necessarily concave. Several examples are investigated where optimal designs with respect to the new criteria are calculated and compared to Bayesian optimal designs based on a uniform and a functional uniform prior.Comment: Keywords: optimal design; Bayesian optimality criteria; non-informative prior; Jeffreys prior; reference prior; polynomial regression; canonical moments; heteroscedasticity Pages: 21 Figures:

Saturated locally optimal designs under differentiable optimality criteria

We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260-1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1263 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Structural optimization of large structural systems by optimality criteria methods

The fundamental concepts of the optimality criteria method of structural optimization are presented. The effect of the separability properties of the objective and constraint functions on the optimality criteria expressions is emphasized. The single constraint case is treated first, followed by the multiple constraint case with a more complex evaluation of the Lagrange multipliers. Examples illustrate the efficiency of the method

Vanishing shortcoming and asymptotic relative efficiency

The shortcoming of a test is the difference between the maximal attainable power and the power of the test under consideration. Vanishing shortcoming, when the number of observations tends to infinity, is therefore an optimality property of a test. Other familiar optimality criteria are based on the asymptotic relative efficiency of the test. The relations between these optimality criteria are investigated. It turns out that vanishing shortcoming is seemingly slightly stronger than first-order efficiency, but in regular cases there is equivalence. The results are in particular applied on tests for goodness-of-fit

Optimality criteria of hybrid inflation-price level targeting

This paper provides a sensitivity analysis of the relative performance of inflation targeting, price level targeting, and hybrid targeting, the combination of these two. A simple, three-period, steady state to steady state economy is presented, where monetary policy is facing various sets of forward and backward looking expectations, social preferences on inflation and output gap stabilization, and degrees of cost push shock persistence. we derive optimal policy mix under the whole spectrum of these economic conditions, reporting also the criteria of the replicability of the theoretically optimal solution. The main intention of the examination is to reveal the nature of each interrelation between economic and policy parameters. The results show that (i) the relative strength of regimes depends heavily on the preconditions, and that (ii) the relationships of parameters related to the performance are non-linear and occasionally non-monotonic as well. our model specification is somewhat restrictive, however, contrary to the related literature, the examination, even in the intermediate cases, can be conducted analytically.hybrid inflation-price level targeting, hybrid new keynesian Phillips curve, cost push shock persistence

Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and coordinate-wise optimality. These conditions are then used to derive three numerical algorithms aimed at finding points satisfying the resulting optimality criteria: the iterative hard thresholding method and the greedy and partial sparse-simplex methods. The first algorithm is essentially a gradient projection method while the remaining two algorithms are of coordinate descent type. The theoretical convergence of these methods and their relations to the derived optimality conditions are studied. The algorithms and results are illustrated by several numerical examples.Comment: submitted to SIAM Optimizatio

Optimal experimental designs for inverse quadratic regression models

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 $E$-criteria, which reflect various aspects of the precision of the maximum likelihood estimator for the parameters in inverse quadratic regression models. In particular it is demonstrated that for a sufficiently large design space geometric allocation rules are optimal with respect to many optimality criteria. Moreover, in numerous cases the designs with respect to the different criteria are supported at the same points. Finally, the efficiencies of different optimal designs with respect to various optimality criteria are studied, and the efficiency of some commonly used designs are investigated.Comment: 24 page