The application of the durbin-watson test to the dynamic regression model under normal and non-normal errors

Until recently, a difficulty with applying the Durbin-Watson (DW) test to the dynamic linear regression model has been the lack of appropriate critical values. Inder (1986) used a modified small-disturbance distribution (SDD) to find approximate critical values. King and Wu (1991) showed that the exact SDD of the DW statistic is equivalent to the distribution of the DW statistic from the regression with the lagged dependent variables replaced by their means. Unfortunately, these means are unknown although they could be estimated by the actual variable values. This provides a justification for using the exact critical values of the DW statistic from the regression with the lagged dependent variables treated as non-stochastic regressors. Extensive Monte Carlo experiments are reported in this paper. They show that this approach leads to reasonably accurate critical values, particularly when two lags of the dependent variable are present. Robustness to non-normality is also investigated.     

Power Allocations: Determining Sample Sizes for Subnational Areas

In many surveys, reliable estimates are required both at the national level and for subnational areas. When the subnational areas vary considerably in population size or importance, problems can arise in the use of standard allocations. In this article, a simple allocation method is suggested for achieving reliable national and subnational estimates.     

On Exact K-optimal Designs Minimizing the Condition Number

A new design criterion based on the condition number of an information matrix is proposed to construct optimal designs for linear models, and the resulting designs are called K-optimal designs. The relationship between exact and asymptotic K-optimal designs is derived. Since it is usually hard to find exact optimal designs analytically, we apply a simulated annealing algorithm to compute K-optimal design points on continuous design spaces. Specific issues are addressed to make the algorithm effective. Through exact designs, we can examine some properties of the K-optimal designs such as symmetry and the number of support points. Examples and results are given for polynomial regression models and linear models for fractional factorial experiments. In addition, K-optimal designs are compared with A-optimal and D-optimal designs for polynomial regression models, showing that K-optimal designs are quite similar to A-optimal designs.     

The inflation–output volatility trade-off: a case where anti-inflation monetary policy turns out to be successful, a historical assessment

Over the period 1988–2000, the Greek monetary authorities seemed to have implemented a successful disinflation policy. The question, however, is whether this disinflation was optimal or not. This paper, through a theoretical model and the GMM approach, constructs an optimal policy frontier in terms of a trade-off between output and inflation variabilities. The frontier yields increases in the output variance when policymakers attempt to decrease inflation variances, and vice versa. The location of the actual monetary policy performance suggests a policy close to the frontier, implying a successful monetary policy.     

Optimal inventory model for items with imperfect quality and shortage backordering

In this study, we develop an optimal inventory model for items with imperfect quality and shortage backordering. Such implicit assumption is reasonable in view of the fact that poor-quality items do exist during production. They are usually picked up during the screening process and are withdrawn from stock instantaneously. It is assumed that all customers are willing to wait for new supply when there is a shortage. The analysis shows that our model is a generalization of the models in current literatures. An algorithm and numerical analysis developed show that our model always results in better performance.     

A note on D-optimal designs for models with and without an intercept

In this paper we give a sufficient condition under which theD-optimal design for a regression model without an intercept can be obtained from theD-optimal design for the corresponding model with an intercept by simply removing the origin from its support points. Examples are given to demonstrate the applications of the results.     

An asymptotic approach to progressive censoring

Progressive Type-II censoring was introduced by Cohen (Technometrics 5(1963) 327) and has been the topic of much research. The question stands whether it is sensible to use this sampling plan by design, instead of regular Type-II right censoring. We introduce an asymptotic progressive censoring model, and find optimal censoring schemes for location-scale families. Our optimality criterion is the determinant of the 2×2 covariance matrix of the asymptotic best linear unbiased estimators. We present an explicit expression for this criterion, and conditions for its boundedness. By means of numerical optimization, we determine optimal censoring schemes for the extreme value, the Weibull and the normal distributions. In many situations, it is shown that these progressive schemes significantly improve upon regular Type-II right censoring.     

环境经济投入产出模型的最优控制

本文根据环境经济投入产出表的基本结构,首先建立环境经济系统中产品与废物的宏观总量的离散差分方程,进而导出其优化模型,最后求出了优化模型的最优反馈控制序列解．     

Near-optimal designs for dual channel microarray studies

Summary.  Much biological and medical research employs microarray studies to monitor gene expression levels across a wide range of organisms and under many experimental conditions. Dual channel microarrays are a common platform and allow two samples to be measured simultaneously. A frequently used design uses a common reference sample to make conditions across different arrays comparable. Our aim is to formulate microarray experiments in the experimental design context and to use simulated annealing to search for near-optimal designs. We identify a subclass of designs, the so-called interwoven loop designs, that seems to have good optimality properties compared with the near-optimal designs that are found by simulated annealing. Commonly used reference designs and dye swap designs are shown to be highly inefficient.