New important developments in small area estimation

The purpose of this paper is to review and discuss some of the new important developments in small area estimation (SAE) methods. Rao (2003) wrote a very comprehensive book, which covers all the main developments in this topic until that time and so the focus of this review is on new developments in the last 7 years. However, to make the review more self contained, I also repeat shortly some of the older developments. The review covers both design based and model-dependent methods with emphasis on the prediction of the area target quantities and the assessment of the prediction error. The style of the paper is similar to the style of my previous review on SAE published in 2002, explaining the new problems investigated and describing the proposed solutions, but without dwelling on theoretical details, which can be found in the original articles. I am hoping that this paper will be useful both to researchers who like to learn more on the research carried out in SAE and to practitioners who might be interested in the application of the new methods

Estimation of treatment effects in observational studies by recovering the assignment probabilities and the population model

In observational studies the assignment of units to treatments is with unknown probabilities. Consequently, estimation and comparison of treatment effects based on the empirical distributions of the response under the various treatments can be biased since units exposed to one treatment could differ in important but unknown characteristics from units exposed to other treatments. In this article we study the plausibility of analyzing observational data by deriving the parametric distribution of the observed response under a given treatment as a function of the distribution that would be obtained under a strongly ignorable assignment, and the assignment process, which is modeled as a function of the observed data (the response and covariate values). The use of this approach is founded by showing that the sample distribution of the observed responses is identifiable under some general conditions. The goodness of fit of this distribution can be tested by using standard test statistics since it refers to the observed data, but we also develop a new test. The proposed approach allows also testing the assumptions underlying the use of methods that employ instrumental variables, or methods that use propensity scores with a given set of covariates.We assess the performance of the proposed approach and compare it to existing approaches using data collected in the year 2000 by OECD for the Programme for International Student Assessment (PISA). In the present application we compare students’ scores in mathematics between public and private schools in Ireland and conclude, somewhat surprisingly, that the public schools perform better than the private schools. This finding is supported by one of the existing methods as well

Ethics and OR: Operationalising Discourse Ethics

Operational researchers help managers decide what they ought to do and yet this is generally evaluated in terms of efficiency or effectiveness, not ethicality. However, the combination of the tremendous power of global corporations and the financial markets, and the problems the world faces in terms of economic and environmental sustainability, has led to a revival of interest in ethical approaches. This paper explores a relatively recent and innovative process called discourse ethics. This is very different from traditional ethical systems in taking ethical decisions away from individuals or committees and putting them in the hands of the actual people who are involved and affected through processes of debate and deliberation. The paper demonstrates that discourse ethics has strong connections to OR, especially in the areas of soft and critical systems, and that OR can actually contribute to the practical operationalisation of discourse ethics. At the same time, discourse ethics can provide a rigorous discursive framework for “ethics beyond the model"

Bootstrap Approximation to Prediction MSE for State-Space Models with Estimated Parameters

We propose a simple but general bootstrap method for estimating the Prediction Mean Square Error (PMSE) of the state vector predictors when the unknown model parameters are estimated from the observed series. As is well known, substituting the model parameters by the sample estimates in the theoretical PMSE expression that assumes known parameter values results in under-estimation of the true PMSE. Methods proposed in the literature to deal with this problem in state-space modelling are inadequate and may not even be operational when fitting complex models, or when some of the parameters are close to their boundary values. The proposed method consists of generating a large number of series from the model fitted to the original observations, re-estimating the model parameters using the same method as used for the observed series and then estimating separately the component of PMSE resulting from filter uncertainty and the component resulting from parameter uncertainty. Application of the method to a model fitted to sample estimates of employment ratios in the U.S.A. that contains eighteen unknown parameters estimated by a three-step procedure yields accurate results. The procedure is applicable to mixed linear models that can be cast into state-space form. (Updated 6th October 2004

State-space modeling with correlated measurements with application to small area estimation under benchmark constraints

The problem of Small Area Estimation is how to produce reliable estimates of area (domain) characteristics, when the sizes within the areas are too small to warrant the use of traditional direct survey estimates. This problem is commonly tackled by borrowing information from either neighboring areas and/or from previous surveys, using appropriate time series/cross-sectional models. In order to protect against possible model breakdowns and for other reasons, it is often required to benchmark the model dependent estimates to the corresponding direct survey estimates in larger areas, for which the survey estimates are sufficiently accurate. The benchmarking process defines another way of borrowing information across the areas.This article shows how benchmarking can be implemented with the state-space models used by the Bureau of Labor Statistics in the U.S. for the production of the monthly employment and unemployment estimates at the state level. The computation of valid estimators for the variances of the benchmarked estimators requires joint modeling of the direct estimators in several states, which in turn requires the development of a filtering algorithm for state-space models with correlated measurement errors. No such algorithm has been developed so far. The application of the proposed procedure is illustrated using real unemployment series

On the Evidence for Axion-like Particles from Active Galactic Nuclei

Burrage, Davis, and Shaw recently suggested exploiting the correlations between high and low energy luminosities of astrophysical objects to probe possible mixing between photons and axion-like particles (ALP) in magnetic field regions. They also presented evidence for the existence of ALP's by analyzing the optical/UV and X-ray monochromatic luminosities of AGNs. We extend their work by using the monochromatic luminosities of 320 unobscured Active Galactic Nuclei from the Sloan Digital Sky Survey/Xmm-Newton Quasar Survey (Young et al., 2009), which allows the exploration of 18 different combinations of optical/UV and X-ray monochromatic luminosities. However, we do not find compelling evidence for the existence of ALPs. Moreover, it appears that the signal reported by Burrage et al. is more likely due to X-ray absorption rather than to photon-ALP oscillation.Comment: 16 pages, 12 figures. Updated to reflect the minor changes introduced in the published versio

Small area estimation of labour force indicators under a multinomial model with correlated time and area effects

[Abstract] The aim of the paper is the estimation of small area labour force indicators like totals of employed and unemployed people and unemployment rates. Small area estimators of these quantities are derived from four multinomial logit mixed models, including a model with correlated time and area random effects. Mean-squared errors are used to measure the accuracy of the estimators proposed and they are estimated by analytic and bootstrap methods. The methodology introduced is applied to real data from the Spanish Labour Force Survey of Galicia.Ministerio de Ciencia e Innovación; MTM2008- 03010Galicia. Consellería de Cultura, Educación e Ordenación Universitaria; CN2012/211Ministerio de Ciencia e Innovación; MTM2012-37077-C02-0

Temporal Variability of the X-ray Emission of the Crab Nebula Torus

We have analyzed five ROSAT HRI images of the Crab Nebula spanning the years 1991 to 1997 and have found significant changes in the emission structure of the X-ray torus surrounding the pulsar. Certain regions increase in brightness by about 20% over the six years, while others show decreases in surface brightness. The origin of these changes is unclear, but a possible explanation is that the bulk velocity of the synchrotron radiating electrons has decreased on the order of 20% as well.Comment: 15 pages plus 6 figures, figure 1 and figure 6 are in color, to appear in The Astrophysical Journal, Jan 1, 1999, Vol. 510, #

Time Variability in the X-ray Nebula Powered by Pulsar B1509-58

We use new and archival Chandra and ROSAT data to study the time variability of the X-ray emission from the pulsar wind nebula (PWN) powered by PSR B1509-58 on timescales of one week to twelve years. There is variability in the size, number, and brightness of compact knots appearing within 20" of the pulsar, with at least one knot showing a possible outflow velocity of ~0.6c (assuming a distance to the source of 5.2 kpc). The transient nature of these knots may indicate that they are produced by turbulence in the flows surrounding the pulsar. A previously identified prominent jet extending 12 pc to the southeast of the pulsar increased in brightness by 30% over 9 years; apparent outflow of material along this jet is observed with a velocity of ~0.5c. However, outflow alone cannot account for the changes in the jet on such short timescales. Magnetohydrodynamic sausage or kink instabilities are feasible explanations for the jet variability with timescale of ~1.3-2 years. An arc structure, located 30"-45" north of the pulsar, shows transverse structural variations and appears to have moved inward with a velocity of ~0.03c over three years. The overall structure and brightness of the diffuse PWN exterior to this arc and excluding the jet has remained the same over the twelve year span. The photon indices of the diffuse PWN and possibly the jet steepen with increasing radius, likely indicating synchrotron cooling at X-ray energies.Comment: accepted to ApJ, 14 pages, 8 figure