8,857 research outputs found
The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem
Threshold Accepting (TA) is a powerful optimization heuristic from the class of stochastic local search algorithms. It has been applied successfully to different optimization problems in statistics and econometrics, including the uniform design problem. Using the latter application as example, the stochastic properties of a TA implementation are analyzed. We provide a formal framework for the analysis of optimization heuristics like TA, which can be used to estimate lower bounds and to derive convergence results. It is also helpful for tuning real applications. Based on this framework, empirical results are presented for the uniform design problem. In particular, for two problem instances, the rate of convergence of the algorithm is estimated to be of the order of a power of -0.3 to -0.7 of the number of iterations. --Heuristic optimization,Threshold Accepting,Stochastic analysis of heuristics
Optimal designs for mixed models in experiments based on ordered units
We consider experiments for comparing treatments using units that are ordered
linearly over time or space within blocks. In addition to the block effect, we
assume that a trend effect influences the response. The latter is modeled as a
smooth component plus a random term that captures departures from the smooth
trend. The model is flexible enough to cover a variety of situations; for
instance, most of the effects may be either random or fixed. The information
matrix for a design will be a function of several variance parameters. While
data will shed light on the values of these parameters, at the design stage,
they are unlikely to be known, so we suggest a maximin approach, in which a
minimal information matrix is maximized. We derive maximin universally optimal
designs and study their robustness. These designs are based on semibalanced
arrays. Special cases correspond to results available in the literature.Comment: Published in at http://dx.doi.org/10.1214/07-AOS518 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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Combining forecasts based on multiple encompassing tests in a macroeconomic core system
Copyright Ā© 2010 John Wiley & Sons, Ltd. This is the accepted version of the following article: Costantini, M. and Kunst, R. M. (2011), Combining forecasts based on multiple encompassing tests in a macroeconomic core system. J. Forecast., 30: 579ā596, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/for.1190/abstract.This paper investigates whether and to what extent multiple encompassing tests may help determine weights for forecast averaging in a standard vector autoregressive setting. To this end we consider a new test-based procedure, which assigns non-zero weights to candidate models that add information not covered by other models. The potential benefits of this procedure are explored in extensive Monte Carlo simulations using realistic designs that are adapted to UK and to French macroeconomic data, to which trivariate vector autoregressions (VAR) are fitted. Thus simulations rely on potential data-generating mechanisms for macroeconomic data rather than on simple but artificial designs. We run two types of forecast ācompetitionsā. In the first one, one of the model classes is the trivariate VAR, such that it contains the generating mechanism. In the second specification, none of the competing models contains the true structure. The simulation results show that the performance of test-based averaging is comparable to uniform weighting of individual models. In one of our role model economies, test-based averaging achieves advantages in small samples. In larger samples, pure prediction models outperform forecast averages
Designs efficiency for non-market valuation with choice modelling: how to measure it, what to report and why
We review the basic principles for the evaluation of design efficiency in discrete choice modelling with a focus on efficiency of WTP estimates from the multinomial logit model. The discussion is developed under the realistic assumption that researchers can plausibly define a prior on the utility coefficients. Some new measures of design performance in applied studies are proposed and their rationale discussed. An empirical example based on the generation and comparison of fifteen separate designs from a common set of assumptions illustrates the relevant considerations to the context of non-market valuation, with particular emphasis placed on C-efficiency. Conclusions are drawn for the practice of reporting in non-market valuation and for future work on design research
Comparing algorithms and criteria for designing Bayesian conjoint choice experiments.
The recent algorithm to find efficient conjoint choice designs, the RSC-algorithm developed by SƔndor and Wedel (2001), uses Bayesian design methods that integrate the D-optimality criterion over a prior distribution of likely parameter values. Characteristic for this algorithm is that the designs satisfy the minimal level overlap property provided the starting design complies with it. Another, more embedded, algorithm in the literature, developed by Zwerina et al. (1996), involves an adaptation of the modified Fedorov exchange algorithm to the multinomial logit choice model. However, it does not take into account the uncertainty about the assumed parameter values. In this paper, we adjust the modified Fedorov choice algorithm in a Bayesian fashion and compare its designs to those produced by the RSC-algorithm. Additionally, we introduce a measure to investigate the utility balances of the designs. Besides the widely used D-optimality criterion, we also implement the A-, G- and V-optimality criteria and look for the criterion that is most suitable for prediction purposes and that offers the best quality in terms of computational effectiveness. The comparison study reveals that the Bayesian modified Fedorov choice algorithm provides more efficient designs than the RSC-algorithm and that the Dand V-optimality criteria are the best criteria for prediction, but the computation time with the V-optimality criterion is longer.A-Optimality; Algorithms; Bayesian design; Bayesian modified Fedorov choice algorithm; Choice; Conjoint choice experiments; Criteria; D-Optimality; Design; Discrete choice experiments; Distribution; Effectiveness; Fashion; G-optimality; Logit; Methods; Model; Multinomial logit; Predictive validity; Quality; Research; RSC-algorithm; Studies; Time; Uncertainty; V-optimality; Value;
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