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Following the British Geological Survey’s (BGS) 1970s – 1990s Mineral Reconnaissance Programme (MRP), there has been limited characterisation and quantification of base and precious metal mineralisation in the UK, with the notable exception of Au. Data gaps still exist regarding mineral paragenesis, geochronology, deportment of critical raw materials (CRM), and ore forming processes. With increased focus on CRM, NetZero, and supply risk we must improve our knowledge of deportment in base metal systems. The BGS Critical Minerals Intelligence Centre (CMIC) was recently established to aid the UK in meeting projected future CRM demand and will act as a nexus for industry and academia. Here, we establish a workflow and document a case study where academia and the CMIC have partnered to re-evaluate a potential mineral resource, a starting point for renewed studies elsewhere in the UK. The Black Stockarton Moor (BSM) post-subduction porphyry Cu system is thought to have formed by interaction of Devonian plutonic to sub-volcanic complexes with Silurian turbidites in the Southern Uplands of Scotland. No study of the BSM has been undertaken since the 1979 MRP report, thus whether it is of any modern value remains unproven. Field sampling and utilising the National Geological Repository at BGS will allow for optical and scanning electron microscopy (SEM) to quantitatively establish paragenesis and primary mineralogy. Sites will then be identified for chemical mapping to quantify CRM deportment in base metals using SEM-energy dispersive X-ray analysis (EDX), with areas of particular interest further quantified by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Focused ion beam (FIB) nano-tomography will be used to identify the cm to nano-scale distribution of CRM. Finally, magmatism and mineralisation will be fully temporally constrained using U-Pb analysis of zircon, titanite, calcite and epidote and/or Re-Os analysis of sulphides as appropriate. On a large scale, this study will address one set of data gaps by re-invigorating our knowledge of the geology and geodynamic associations of mineralisation. However, by also identifying the quantities and associations of metals at the cm to micron scale, it addresses another, by constraining the extent and nature of processes responsible for the distribution of metals in such deposits. This workflow is to be refined for application to mineralisation elsewhere in the UK including work underway on the Strontian Caledonian granite and associated Pb-Zn mineralisation in the Northern Scottish Highlands.

Plutons formed during the latter stages of the Caledonian Orogeny are a prominent feature of the landscape of the Northern Highlands of Scotland. Despite their prominence, and in rare cases mineralisation (Strontian) or high heat producing properties (Helmsdale), various intrusions lack critical analysis of their timing, emplacement mechanisms and geodynamic significance. For example, published emplacement ages are typically from small air abrasion isotope dilution studies of the 1970’s-1990’s1. These have recently been argued to risk bias towards high quality grains which potentially grew during lower crustal processing of parental magmas2. Here, we are conducting U-Pb zircon re-dating of six intrusions associated with the Great Glen Fault system: Glen Loy, Linnhe, Abriachan, Cluanie, Strontian and Helmsdale. Through a combination of extensive zircon picking, cathodoluminescence imaging and laser ablation mass spectrometry on multiple points per zircon we aim to reduce this selection bias. Initial results, with titanite geochronology to follow, indicate that Glen Loy and Cluanie pre-date Iapetus slab breakoff and are therefore related to subduction beneath the Laurentian margin. All plutons studied so far demonstrate evidence of zircon growth which pre-dates final emplacement. We argue that, Iapetus subduction and Baltica-Laurentia collision were responsible for the generation of a lower crustal hot zone beneath the Northern Highlands. This hot zone lasted from ~450-430 Ma, prior to the upsurge in magmatism which followed slab breakoff. Re-dating of the ‘outer’ granodiorite facies of the Strontian pluton has produced a probable emplacement age at least 10 Myr younger than the previous accepted age of ~425 Ma. This finding raises questions about a) whether previous results reflected antecrystic zircon and titanite and b) the association of pluton emplacement with the timing of left-lateral motion on the Great Glen Fault system. In addition, few Northern Highlands plutons are significantly mineralised, except for the Pb-Zn-hosting carbonate veins at the Strontian pluton. However, we do not know the age of mineralisation or its metal distributions, particularly any metals which have been designated as critical to society since surveys in the 1980's. In this study, we have also developed a workflow in collaboration with the Critical Minerals Intelligence Centre of the British Geological Survey to date mineralisation using U-Pb methods on calcite, and to compare results with U-Pb apatite dating of a mafic sub-volcanic dyke at the Strontian pluton, suspected to be Permian-Carboniferous in age. We will further address the distribution of metals using a combination of optical petrology, electron microscopy, laser rastering and focused ion beam nano-tomography. This further addresses the above knowledge gaps with correlative cm- to nano-scale and three-dimensional insights into the mineralisation process, a strategy that can be replicated for other potential critical element bearing deposits.

Models of mortality often require constraints in order that parameters may be estimated uniquely. It is not difficult to find references in the literature to the “identifiability problem”, and papers often give arguments to justify the choice of particular constraint systems designed to deal with this problem. Many of these models are generalised linear models, and it is known that the fitted values (of mortality) in such models are identifiable, i.e., invariant with respect to the choice of constraint systems. We show that for a wide class of forecasting models, namely ARIMA $(p,\delta, q)$ models with a fitted mean and $\delta = 1$ or 2, identifiability extends to the forecast values of mortality; this extended identifiability continues to hold when some model terms are smoothed. The results are illustrated with data on UK males from the Office for National Statistics for the age-period model, the age-period-cohort model, the age-period-cohort-improvements model of the Continuous Mortality Investigation and the Lee–Carter model.

The Age-Period-Cohort-Improvement (APCI) model is a new addition to the canon of mortality forecasting models. It was introduced by Continuous Mortality Investigation as a means of parameterising a deterministic targeting model for forecasting, but this paper shows how it can be implemented as a fully stochastic model. We demonstrate a number of interesting features about the APCI model, including which parameters to smooth and how much better the model fits to the data compared to some other, related models. However, this better fit also sometimes results in higher value-at-risk (VaR)-style capital requirements for insurers, and we explore why this is by looking at the density of the VaR simulations.

Many common models of mortality can be expressed compactly in the language of either generalized linear models or generalized non-linear models. The R language provides a description of these models which parallels the usual algebraic definitions but has the advantage of a transparent and flexible model specification. We compare eight model structures for mortality. For each structure, we consider (a) the Poisson models for the force of mortality with both log and logit link functions and (b) the binomial models for the rate of mortality with logit and complementary log–log link functions. Part of this work shows how to extend the usual smooth two-dimensional P-spline model for the force of mortality with Poisson error and log link to the other smooth two-dimensional P-spline models with Poisson and binomial errors defined in (a) and (b). Our comments are based on the results of fitting these models to data from six countries: Australia, France, Japan, Sweden, UK and USA. We also discuss the possibility o...

We consider a generalized linear model (GLM) with canonical link function in which parameters can be subject to (i) a set of linear constraints and (ii) smoothing. We apply Lagrange methods to give a general Newton-Raphson algorithm for such a GLM in which parameters are estimated, constraints are applied and smoothing is performed simultaneously. We express the Lee-Carter model, an important model for the forecasting of human mortality, in terms of GLMs, and use our method to estimate the parameters in the model. The smoothing option allows us to improve the forecasting properties of the model. We compare the performance of (i) the Poisson model with log link for the force of mortality and (ii) the binomial model with logit link for the probability of death in a calendar year. Examples using UK Office for National Statistics data are provided.

Longevity risk faced by annuity portfolios and defined-benefit pension schemes is typically long-term, i.e. the risk is of an adverse trend which unfolds over a long period of time. However, there are circumstances when it is useful to know by how much expectations of future mortality rates might change over a single year. Such an approach lies at the heart of the one-year, value-at-risk view of reserves, and also for the pending Solvency II regime for insurers in the European Union. This paper describes a framework for determining how much a longevity liability might change based on new information over the course of one year. It is a general framework and can accommodate a wide choice of stochastic projection models, thus allowing the user to explore the importance of model risk. A further benefit of the framework is that it also provides a robustness test for projection models, which is useful in selecting an internal model for management purposes.

This paper proposes an XML format for standard Z. We describe several earlier XML proposals for Z, the problems and issues that arose, and the rationales behind our new proposal. The new proposal is based upon a comparison of various existing Z annotated syntaxes, to ensure that the mark-up will be widely usable. This XML format is expected to become a central feature of the CZT (Community Z Tools) initiative.

The potential instability of a fixed monetary rule combined with automatic fixed stabilisers is a well-established feature of closed economy IS/LM models with wealth effects and asset accumulation. This paper examines the stability issue in a general open economy macromodel with alternative expectations mechanisms (rational or adaptive) in both the labour market and the foreign exchange market. The fixed monetary rule is found to be stabilising only in special cases, notably when post-tax real interest rates are negative and the foreign exchange market is characterised by high capital mobility and rational expectations. By contrast, the alternative rule of fixing the rate of growth of nominal government debt is stable for a wide range of parameter values and alternative expectations schemes.

This paper examines two schemes for the international coordination of macroeconomic policy using a world econometric model, the National Institute Global Econometric Model. The first is the extended target zone scheme proposed by J. Williamson and M. Miller (1987), which involves targeting fundamental equilibrium exchange rates using monetary policy and using fiscal policy to control domestic demand. The second uses fiscal policy to target the current account and monetary policy to stabilize domestic demand. Both schemes are parameterized using optimal control techniques on the National Institute Global Econometric Model, and the welfare gains in using these schemes compared to historical experience from 1974 to 1986 are assessed.

Mortality data are often classified by age at death and year of death. This classification results in a heterogeneous risk set and this can cause problems for the estimation and forecasting of mortality. In the modelling of such data, we replace the classical assumption that the numbers of claims follow the Poisson distribution with the weaker assumption that the numbers of claims have a variance proportional to the mean. The constant of proportionality is known as the dispersion parameter and it enables us to allow for heterogeneity; in the case of insurance data the dispersion parameter also allows for the presence of duplicates in a portfolio. We use both the quasi-likelihood and the extended quasi-likelihood to estimate models for the smoothing and forecasting of mortality tables jointly with smooth estimates of the dispersion parameters. We present three main applications of our method: first, we show how taking account of dispersion reduces the volatility of a forecast of a mortality table; second, we smooth mortality data by amounts, ie, when deaths are amounts claimed and exposed-to-risk are sums assured; third, we present a joint model for mortality by lives and by amounts with the property that forecasts by lives and by amounts are consistent. Our methods are illustrated with data from the Continuous Mortality Investigation.

This paper describes a new empirical model of Latin America built to study North-South macroeconomic interactions. Special attention is paid to the supply-side determination of the natural rate of output and to asset accumulation. The model's properties are presented both empirically and by means of analytical representation. The model is used to examine the effects of global shocks on Latin America as simulated by the LBS/NIESR Global Econometric Model (GEM). In particular, the authors assess the relative impact of OECD monetary contraction and lack of fiscal policy coordination on the continent in the 1980s. Coauthors are David Currie, T. G. Srinivasan and David Vines. Copyright 1992 by Blackwell Publishers Ltd and The Victoria University of Manchester

Christopher Thomas Blaiklock (“Chris”) intended to be a physician and passed the MRCP before changing his mind and training as a surgeon. He was a registrar in neurosurgery at Atkinson Morley Hospital when the first …

Several important classes of liability are sensitive to the direction of future mortality trends, and this paper presents some recent developments in fitting smooth models to historical mortality-experience data. We demonstrate the impact these models have on mortality projections, and the resulting impact which these projections have on financial products. We base our work round the Lee-Carter family of models. We find that each model fit, while using the same data and staying within the Lee-Carter family, can change the direction of the mortality projections. The main focus of the paper is to demonstrate the impact of these projections on various financial calculations, and we provide a number of ways of quantifying, both graphically and numerically, the model risk in such calculations. We conclude that the impact of our modelling assumptions is financially material. In short, there is a need for awareness of model risk when assessing longevity-related liabilities, especially for annuities and pensions.

Changes in emotional and social behaviour are relatively common following traumatic brain injury (TBI). Impairments in recognising the emotional state of others may underlie some of the problems in social relationships that these patients experience. The few previous studies examining emotion recognition in TBI typically assessed patients once, long after the onset of brain injury, making it difficult to distinguish the direct effect of brain injury from the effects of environmental changes. This study examined 30 patients with TBI shortly after brain injury and 32 orthopaedic control patients on their recognition of emotions expressed in the face and the voice using discrimination and labelling tasks. These patients were followed up 1 year later to examine the longitudinal development of emotion recognition deficits. TBI patients were found to be impaired on emotion recognition compared to the control patients both early after injury and 1 year later. The fact that impairments in emotion recognition were evident early after TBI and no evidence of recovery over time was found, suggests a direct effect of brain injury.

The solution structure of plasmid DNA is known to be a strong function of solution conditions due to intramolecular electrostatic interactions between the charged phosphate groups along the DNA backbone. The objective of this work was to determine whether it was possible to enhance the use of ultrafiltration for separation of different plasmid isoforms by proper selection of the solution ionic strength and ion type. Experiments were performed with a 3.0 kbp plasmid using composite regenerated cellulose ultrafiltration membranes. The transmission of the linear isoform was nearly independent of solution ionic strength, but increased significantly with increasing filtrate flux due to the elongation of the highly flexible plasmid in the converging flow field into the membrane pores. In contrast, the transmission of the open-circular and supercoiled plasmids both increased with increasing NaCl or MgCl2 concentration due to the change in plasmid size and conformational flexibility. The effect of ionic strength was greatest for the supercoiled plasmid, providing opportunities for enhanced purification of this therapeutically active isoform. This behavior was confirmed using experiments performed with binary mixtures of the different isoforms. These results clearly demonstrate the potential for enhancing the performance of membrane systems for plasmid DNA separations by proper selection of the ionic conditions.

Summary Data with an array structure are common in statistics, and the design or regression matrix for analysis of such data can often be written as a Kronecker product. Factorial designs, contingency tables and smoothing of data on multidimensional grids are three such general classes of data and models. In such a setting, we develop an arithmetic of arrays which allows us to define the expectation of the data array as a sequence of nested matrix operations on a coefficient array. We show how this arithmetic leads to low storage, high speed computation in the scoring algorithm of the generalized linear model. We refer to a generalized linear array model and apply the methodology to the smoothing of multidimensional arrays. We illustrate our procedure with the analysis of three data sets: mortality data indexed by age at death and year of death, spatially varying microarray background data and disease incidence data indexed by age at death, year of death and month of death.

Late-life mortality patterns are of crucial interest to actuaries assessing longevity risk. One important explanatory variable is year of birth. We present the results of various analyses demonstrating this, including a statistical model which lends weight to the importance of year-of-birth effects in both population and insured data. We further find that a model based on age and year of birth fits United Kingdom mortality data better than a model based on age and period, suggesting that cohort effects are more significant than period effects. The financial implications of these cohort effects are considerable for portfolios with long-term longevity exposure, such as annuities written by insurance companies and defined benefit pension schemes.

Symbolic simulation and uninterpreted functions have long been staple techniques for formal hardware verification. In recent years, we have adapted these techniques for the automatic, formal verification of low-level embedded software--specifically, checking the equivalence of different versions of assembly language programs. Our approach, though limited in scalability, has proven particularly promising for the intricate code optimizations and complex architectures typical of high-performance embedded software, such as for DSPs and VLIW processors. Indeed, one of our key findings was how easy it was to create or retarget our verification tools to different, even very complex, machines. The resulting tools automatically verified or found previously unknown bugs in several small sequences of industrial and published example code. This paper provides an introduction to these techniques and a review of our results.

A framework of penalized generalized linear models and tensor products of B-splines with roughness penalties allows effective smoothing of data in multidimensional arrays. A straightforward application of the penalized Fisher scoring algorithm quickly runs into storage and computational difficulties. A novel algorithm takes advantage of the special structure of both the data as an array and the model matrix as a tensor product; the algorithm is fast, uses only a moderate amount of memory and works for any number of dimensions. Examples are given of how the method is used to smooth life tables and image data.

The prediction of future mortality rates is a problem of fundamental importance for the insurance and pensions industry. We show how the method of P-splines can be extended to the smoothing and forecasting of two-dimensional mortality tables. We use a penalized generalized linear model with Poisson errors and show how to construct regression and penalty matrices appropriate for two-dimensional modelling. An important feature of our method is that forecasting is a natural consequence of the smoothing process. We illustrate our methods with two data sets provided by the Continuous Mortality Investigation Bureau, a central body for the collection and processing of UK insurance and pensions data.

In the developed world, trauma is the principal cause of death under the age of 40 and is the third largest overall killer. In the UK, approximately 25,000 people die each year as a result of major injury, 25% as a result of head injuries alone. Despite improved diagnosis and management, infection remains the commonest complication in those patients surviving the initial injury. Some 5% are reported to die as a result of septic complications. Prolonged periods of intensive care and respiratory support predispose to infective respiratory complications. These patients in the absence of significant systemic injury and, as a result of severe head injury, are unable to mount an effective immune response. This literature review examines the changes that have been reported to occur in the immune system following isolated severe head injury and explores the relationship these changes may have to the increased development of infective complications.

We consider additive models with k smooth terms and correlated errors, and use the penalised spline approach of Eilers & Marx (1996) to estimate the smooth functions. We obtain explicit expressions for the hat-matrix of the model and each individual curve. P-splines are represented as mixed models and REML is used to select the smoothing and correlation parameters. The method is applied to the analysis of some time series data.

The radical changes instituted in the regulation of privatized public utilities in the UK in the 1980s and early 1990s have been the subject of extensive discussion, and have been partly instrumental in the development of 'regulatory economics' more widely. In this paper we argue that the conventional economics of regulation, based on principal-agent and related perspectives, treat the issue too narrowly and statically. Drawing on organizational sociology and cooperative game theory, we contend that it is essential to understand the process by which the interaction between the regulator and the regulated firms evolves. Using interview and documentary data, the paper describes the evolution of this relationship in three sectors in the UK. The growth of cooperative informal relationships between regulators and regulatory functions within firms involves the emergence and development of 'regulatory expertise'. This generates advantages for both sides, which are examined in terms of different regulatory games involving different levels of trust. The implications both for institutional design and for the economic theory of regulation are assessed. Copyright 2003, Oxford University Press.

The endemic Seychelles Scops-owl Otus insularis is a Critically Endangered restricted range species currently only recorded in the upland forest of Mahé, the largest (152 km2) and highest (903 m) island in the granitic Seychelles. We studied the response of colour-ringed individuals to playback of conspecific calls, to determine factors affecting playback reaction, to monitor behaviour and to assess the reliability of current monitoring techniques. Playback of the territorial waugh call was conducted at fixed points (c. 200 m apart) every month along a total transect length of 8.4 km between April 1999 and May 2001. On the basis of responses and movements of marked individuals we identified 12 territories and noted their boundaries. Mean territory length was 2.92 points (approximately 400 m), equivalent to a conservative estimated territory size of c. 12–16 ha. Males were more frequently detected than females/pairs. The probability of detection (males vs. females/pairs) was 0.87 vs. 0.50 on territory; 0.65 vs. 0.26 at fixed points within territories; and 0.58 vs. 0.22 at fixed points along the transect. There was some significant seasonal variation in detection rates at fixed points within territories for both males and pairs, and in general there was a low probability of detecting individuals around June-August and a high probability of detection around April and, to a lesser degree, October. Response times and owl-recorder distances were not influenced by moon phase or time of playback. This study provides the first baseline data on individual responses to the systematic repeated use of playback in Seychelles Scops-owl. We discuss the implications for current monitoring and its application to other similar Otus species.

We consider the application of P-splines (Eilers and Marx, 1996) to three classes of models with smooth components: semiparametric models, models with serially correlated errors, and models with heteroscedastic errors. We show that P-splines provide a common approach to these problems. We set out a simple nonparametric strategy for the choice of the P-spline parameters (the number of knots, the degree of the P-spline, and the order of the penalty) and use mixed model (REML) methods for smoothing parameter selection. We give an example of a model in each of the three classes and analyse appropriate data sets.

A joint model for plot yield in response to fertility trends and interplot competition is described. The model combines the mixed model representation of a cubic smoothing spline to model fertility and a regression model with auto-regressive terms to model competition. Estimation is based on a generalization of residual maximum likelihood. The methods were applied to a series of 70 sugar beet trials conducted by the Plant Breeding Institute, Cambridge, UK, and the results summarized.

We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log-likelihood score function. For the variance components model, we obtain the adjusted profile log-likelihood and show that it equals the restricted log-likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.

This article, based on the first of the 1999 Stockton Lectures, argues that the effective management of the global economy cannot be left to government: that international corporations have a crucial role too. Corporations that play this role can shape and be ahead of the public policy curve and thereby often gain competitive advantage. The public policy game between governments and international business can be co-operative and a positive sum game. If it is not, both sides will be weakened. Success is likely to elude companies adopting strategies that run against the grain of public policy. marketplace, and that it is to society’s benefit that they should so do.

This article assesses the main issues for the energy industry over the next decade, and particularly for the British gas industry. Supporting a carbon tax as a way of counteracting market trends towards lower energy prices, the author argues that the agreements at the Kyoto summit will lead, within a decade, to "an effective framework for restricting greenhouse gases". He welcomes the British Government’s recent consultative document on utility regulation and calls for the gas industry to provide serious analysis to allay concerns about diversity of supply in Britain. He foresees accelerating liberalisation in the EU, based not on central agreement but on a Jeffersonian process whereby regulatory changes in one EU state lead to pressure for similar changes in neighbouring states. He concludes by speculating about the energy industry’s equivalent of the PC or mobile phone.

The aim of this study was to examine the effects of forest fragmentation on the ability of parent birds to provide their young with an adequate food supply. To examine whether prey population densities of the great tit (Parus major L.) and the blue tit (P. caeruleus L.) vary between study areas in different forest size classes we compared provisioning rates and chick diet and related these parameters to breeding success. We filmed 217 nests over two breeding seasons and collected data on frass fall as a general estimate of caterpillar availability. Nests which were attended by none or one parent only during filming (n = 46) were excluded from the analyses. In both years and for both species feeding rates were highest in the smallest fragments and lowest in the large forest. There was also a suggestion that differences in feeding rates between areas vary between years. We found no consistent tendency for prey size to change with forest size, although both species brought slightly smaller prey items to the nest in the smallest forest fragments and feeding rates correlated negatively with prey size. Caterpillars were the main item fed to nestlings, in both species. We found no evidence to suggest that either frass fall or the proportion of caterpillars in the diet varied with forest size. There was also no correlation between mean frass fall and the total number of caterpillars brought to the nests, in either species. Breeding success, as measured by clutch size, brood size, fledging weight and fledging success, did not differ between the small fragments and the large forest, in either species. There was also no relationship between provisioning rate (as concerns volume of prey fed to nestlings and the quality of chick diet) and breeding success parameters. In conclusion, this study does not suggest suboptimal foraging or breeding conditions in small fragments compared to a nearby large forest, for either species.

How the reforms to the U.K. competition regime and the creation of the CMA will enable us to deliver “marked improvements†and meet the expectations on us to enhance the rigor of decision-making and to make more decisions, more quickly, with no attendant drop in quality.

EMU is the historic issue facing the Labour Government. In this article, David Currie considers the prospects for EMU and the challenges that it poses for the Government, particularly in the light of the forthcoming UK Presidency. He also considers the implications and risks of the Chancellor’s recent statement on EMU.

This article calls on companies – and governments – in Europe to welcome competition in their markets. Liberalisation of Europe’s utility sectors has lagged behind the Single Market generally, to the detriment of consumers and industrial users – except in telecommunications where new technology has forced the pace. The author argues that the potential advantages for incumbents of loss of domestic market dominance are outweighed by the advantages of embracing competition and access to overseas markets: they benefit from the discipline of benchmarking, lessened regulatory pressures and fewer barriers to access to markets abroad. He compares the strategies of Electricite de France and British Telecom to illustrate this.

The Extended Target Zone (ETZ) proposal for economic policy coordination is quantitatively assessed and compared with a number of alternative schemes that do not adopt explicit exchange rate targeting. The main finding of the paper is that if exchange rate volatility matters, then the ETZ scheme is clearly superior to the alternatives compared here. However, an important qualification is the high degree of fiscal activism required to prevent output and inflation from deviating from target levels in order to offset the active monetary policy employed to achieve the exchange rate targets. Moreover, when this is combined with an uneven distribution of welfare gains and associated incentive compatibility problems, the ETZ scheme may become unsustainable leading to a breakdown of cooperation.

SUMMARY We consider Buckley-James estimation in simple linear regression applied to the Stanford heart transplant data. We describe an experiment in which the ages of patients are perturbed. The number of limiting values of Buckley-James estimates exhibits chaotic behaviour. By considering the ordering of the residuals we obtain formulae for the limiting values of the regression coefficients.