Combining information for prediction in linear regression

This article deals with the prediction problem in linear regression where the measurements are obtained using k different devices or collected from k different independent sources. For the case of k=2, a Graybill-Deal type combined estimtor for the regression parameters is shown to dominate the individual least squares estimators under the covariance criterion. Two predictors ŷ _c and ŷ _p are proposed. ŷ _c is based on a combined estimator of the regression coefficient vector, and ŷ _p is obtained by combining the individual predictors from different models. Prediction mean square errors of both predictors are derived. It is shown that the predictor ŷ _p is better than the individual predictors for k≥2 and the predictor ŷ _c is better than the individual predictors for k=2. Numerical comparison between ŷ _c and ŷ _p shows that the former is superior to the latter for the case k=2.     

Evaluating FOMC forecasts

Monetary policy outcomes have improved since the early 1980s. One factor contributing to the improvement is that Federal Reserve policymakers began reporting economic forecasts to Congress in 1979. These forecasts indicate what the Federal Open Market Committee (FOMC) members think will be the likely consequence of their policies. We evaluate the accuracy of the FOMC forecasts relative to private sector forecasts, the forecasts of the Research Staff at the Board of Governors, and a naïve alternative. We find that the FOMC output forecasts were better than the naïve model and at least as good as those of the private sector and the Fed staff. The FOMC inflation forecasts were more accurate than the private sector forecasts and the naïve model; for the period ending in 1996, however, they were not as accurate as Fed staff inflation forecasts.     

Predicting the geo-temporal variations of crime and disorder

Traditional police boundaries—precincts, patrol districts, etc.—often fail to reflect the true distribution of criminal activity and thus do little to assist in the optimal allocation of police resources. This paper introduces methods for crime incident forecasting by focusing upon geographical areas of concern that transcend traditional policing boundaries. The computerised procedure utilises a geographical crime incidence-scanning algorithm to identify clusters with relatively high levels of crime (hot spots). These clusters provide sufficient data for training artificial neural networks (ANNs) capable of modelling trends within them. The approach to ANN specification and estimation is enhanced by application of a novel and noteworthy approach, the Gamma test (GT).     

Consistent estimation in the bilinear multivariate errors-in-variables model

A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A∈ℝ^m×n, B∈ℝ^p×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case.  An adjusted least squares estimator is constructed, which converges to the true value X, as m →∞, q →∞. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study. Acknowledgements. We thank two anonymous reviewers for their suggestions and corrections.? A. Kukush is supported by a postdoctoral research fellowship of the Belgian office for Scientific, Technical and Cultural Affairs, promoting Scientific and Technical Collaboration with Central and Eastern Europe.? S. Van Huffel is a full professor with the Katholieke Universiteit Leuven.? I. Markovsky is a research assistant with the Katholieke Universiteit Leuven.? This paper presents research results of the Belgian Programme on Interuniversity Poles of Attraction (IUAP V-22), initiated by the Belgian State, Prime Minister's Office – Federal Office for Scientific, Technical and Cultural Affairs of the Concerted Research Action (GOA) projects of the Flemish Government MEFISTO-666 (Mathematical Engineering for Information and Communication Systems Technology), of the IDO/99/03 project (K.U. Leuven) “Predictive computer models for medical classification problems using patient data and expert knowledge”, of the FWO projects G.0078.01, G.0200.00, and G0.0270.02.? The scientific responsibility is assumed by its authors.     

国际资本流动的新特点与我国利用外资的基本思路

中国正式加入WTO，标志着中国对外开放进入了一个新的阶段，本文试图在分析国际资本流动的新特点的基础上，从完善市场经济制度和投资环境，引资方式创新，发挥利用外资对结构调整战略的配合作用，以及利用外资与宏观经济目标的相互协调等方面，提出中国利用外资的基本思路。     

Forecasting residential burglary

Following the work of Dhiri et al. [Modelling and predicting property crime trends. Home Office Research Study 198 (1999). London: HMSO] at the Home Office predicting recorded burglary and theft for England and Wales to the year 2001, econometric and time series models were constructed for predicting recorded residential burglary to the same date. A comparison between the Home Office econometric predictions and the less alarming econometric predictions made in this paper identified the differences as stemming from the particular set of variables used in the models. However, the Home Office and one of our econometric models adopted an error correction form which appeared to be the main reason why these models predicted increases in burglary. To identify the role of error correction in these models, time series models were built for the purpose of comparison, all of which predicted substantially lower numbers of residential burglaries. The years 1998–2001 appeared to offer an opportunity to test the utility of error correction models in the analysis of criminal behaviour. Subsequent to the forecasting exercise carried out in 1999, recorded outcomes have materialised, which point to the superiority of time series models compared to error correction models for the short-run forecasting of property crime. This result calls into question the concept of a long-run equilibrium relationship for crime.     

An investigation of transformation-based prediction interval for the Weibull median life

Statistical inference based on the Weibull distribution, a distribution widely used in reliability and survival analysis, is usually difficult as it often involves numerical computation and approximation. However, this distribution can be transformed to near-normality by a simple power transformation. Based on this transformation, a prediction interval (PI) for its median can be easily constructed through an inverse transformation. The procedure for selecting the best power transformation through minimizing Kullback-Leibler information is described. The property of this transformation-based PI is investigated. Simple correction factors are also proposed. It is shown that the transformation-based PI with corrections performs well, irrespective of the sample size and parameter values. Simulation results show that the new PI generally outperforms the existing PI. Numerical examples are given for illustration.     

Optimality conditions¶and bubbles in sequential economies¶and bounded relative risk-aversion

We provide specific qualifications in order that Kuhn–Tucker type Euler equations and transversality conditions at infinity hold in stochastic equilibrium models with heterogeneous agents and where assets are traded in sequential markets. It is not assumed that uncertainty is modeled as an event-tree structure or that preferences are necessarily bounded. We also describe an important class of preferences based on bounded relative risk aversion which yields relevant simplifications. Our results are used to establish conditions that rule out asset pricing bubbles. Specific examples of economies with bubbles are also discussed. Received: 28 January 2002 / Accepted: 19 July 2002 We are grateful to the editor and an anonymous referee for their valuable comments. This research was partially supported by MURST (Italy), National Group on “Nonlinear Dynamics and Stochastic Models in Economics and Finance”.     

Endogenous Growth and Negative Externalities

Received March 5, 2001; revised version received August 5, 2002 Published online: April 30, 2003