Numerical Maximisation of Likelihood: A Neglected Alternative to EM?

There is by now a long tradition of using the EM algorithm to find maximum‐likelihood estimates (MLEs) when the data are incomplete in any of a wide range of ways, even when the observed‐data likelihood can easily be evaluated and numerical maximisation of that likelihood is available as a conceptually simple route to the MLEs. It is rare in the literature to see numerical maximisation employed if EM is possible. But with excellent general‐purpose numerical optimisers now available free, there is no longer any reason, as a matter of course, to avoid direct numerical maximisation of likelihood. In this tutorial, I present seven examples of models in which numerical maximisation of likelihood appears to have some advantages over the use of EM as a route to MLEs. The mathematical and coding effort is minimal, as there is no need to derive and code the E and M steps, only a likelihood evaluator. In all the examples, the unconstrained optimiser nlm available in R is used, and transformations are used to impose constraints on parameters. I suggest therefore that the following question be asked of proposed new applications of EM: Can the MLEs be found more simply and directly by using a general‐purpose numerical optimiser?     

公路桥型力学分类及其特点

以力学理论为基础将桥梁桥型进行分类,强调各种桥型的特点及受力特征,并介绍目前国内各种桥型取得的既有成就及桥梁发展趋势。     

On efficiency of the ratio estimator

Summary The exact mean square error for the ratio estimator of a finite population total based on simple random sampling without replacement is shown to have an expected value less than that of the variance of the ratio estimator based on Midzuno’s scheme, under a usual super-population model.     

普通似然及经验似然情况下的结点问题

本文在普通似然及经验似然情况下,分别对数据无结点和有结点的情况做了计算,得出在普通似然及经验似然问题中,有结点与无结点情况完全相同的结论。     

对小地区失业统计差额比的推定

本文对韩国国内行政区域如市郡区等小地区的失业统计共同差额比进行推定的方法有联合推定量,Woolf推定量和Mantel-Haenszel推定量等。对这个推定量的可信度是通过偏差和平均平方误差的概念来进行比较的。从对京畿地区经济活动人口调查情况看,这个地区内的24个市郡单位行政自治地区的男、女失业率差额比的偏差及平均平方误差是通过本次研究提出的推定程序来推定的。这些推定数的稳定性和效率性可以通过相对偏差和相对平均误差平方根来评价。Woolf推定量或Mantel-Haenszel推定量比联合推定量更为稳定,从其效率性来看三者很相似。     

Pseudo empirical likelihood method in the presence of missing data

In this paper, we propose an estimator for the population mean when some observations on the study and auxiliary variables are missing from the sample. The proposed estimator is valid for any unequal probability sampling design, and is based upon the pseudo empirical likelihood method. The proposed estimator is compared with other estimators in a simulation study.     

Forecasting performances of three automated modelling techniques during the economic crisis 2007–2009

In this work we consider the forecasting of macroeconomic variables during an economic crisis. The focus is on a specific class of models, the so-called single hidden-layer feed-forward autoregressive neural network models. What makes these models interesting in the present context is the fact that they form a class of universal approximators and may be expected to work well during exceptional periods such as major economic crises. Neural network models are often difficult to estimate, and we follow the idea of White (2006) of transforming the specification and nonlinear estimation problem into a linear model selection and estimation problem. To this end, we employ three automatic modelling devices. One of them is White’s QuickNet, but we also consider Autometrics, which is well known to time series econometricians, and the Marginal Bridge Estimator, which is better known to statisticians. The performances of these three model selectors are compared by looking at the accuracy of the forecasts of the estimated neural network models. We apply the neural network model and the three modelling techniques to monthly industrial production and unemployment series from the G7 countries and the four Scandinavian ones, and focus on forecasting during the economic crisis 2007–2009. The forecast accuracy is measured using the root mean square forecast error. Hypothesis testing is also used to compare the performances of the different techniques.     

Leaving EMU: a real options perspective

The real option implicit in a country's decision of whether to leave an existing monetary union when there is uncertainty over the future benefits of this move is examined. The theoretical model used is calibrated for the current Euro-12 area by proxying policymakers’ inflation preferences with unemployment rates and debt-to-GDP ratios. A robust group of countries is observed that would choose to remain within EMU consisting of Belgium, Finland, Greece and Italy; France and Spain loosely also belong to this core. Only Luxembourg would robustly want to leave EMU; Ireland and The Netherlands, however, complement that core closely.