Outliers and order statistics

Outliers are to be found among the extremes of a data set. Extremes are examples of order statistics. It is thus relevant to ask to what extent the statistical methods (and probabilistic properties) of outliers and of order statistics coincide and depend on each other. Whilst clear overlap is identifiable, aims and procedures are often quite distinct and each topic plays its own important role in the panoply of statistical principles and methodology.     

The problem of outlier tests in sample surveys

Outliers can occur as readily in samples from the finite populations (e.g. in sample surveys) as in samples from infinite populations. However, in the vast literature on outliers there is almost no mention of outlier tests for data from sample surveys. We examine the behaviour of some standard outlier test statistics for infinite populations when these are applied to finite populations, examining their properties by extensive simulation studies. Some anomalous results are obtained Nsuggesting a fundamental difficulty in testing outliers for the finite population case.     

Social security in the USSR

Social security systems reflect the political and economic realities of their country. The history of the Soviet social security system lends support to this thesis. Its basic features were drawn during Stalin's forceful drive towards heavy industrialization and they remained pretty much the same over the years despite many changes, often of significant detail. It was a system financed by the state, providing earnings-related benefits to workers who fulfilled their work obligations and favouring those in the Communist Party, government and industry whose contribution was deemed to be most useful to the state and the economy. The absence of political freedom meant that open criticism of existing provisions was very difficult, while the emphasis of successive governments on defence and space exploration inevitably meant that state funds for social security suffered and with them the level and range of benefits. The collapse of the Soviet Union has resulted in widespread hardship among those relying on benefits and has created a situation where new social security systems are needed to reflect the new political and economic realities.     

Football spectator behaviour in Argentina: a case of separate evolution

There has been a separate and distinctive evolution of football related violence in Argentina. Fighting between rival gangs of fans in Argentina developed independently and considerably in advance of the modern phenomenon of football hooliganism in Britain. This case is argued using Argentine sources not previously translated into English. The distinctive features of Argentine football violence are described and the main differences in relation to England are outlined. Of paramount importance are the explicit political links of Argentine football clubs. Organised football preceeded democratic politics in Argentina which resulted in the new political parties utilising the football infrastructure of neighbourhood-based clubs. The death rate associated with Argentine football is significantly higher than in England, and the role of the police is more negative in Argentina. In the conclusion a framework is proposed for the comparative and historical analysis of football related violence.     

A Shape-based Glaucoma Index for Tomographic Images

We examine the use of Confocal Laser Tomographic images for detecting glaucoma. From the clinical aspect, the optic nerve head's (ONH) area contains all the relevant information on glaucoma. The shape of ONH is approximately a skewed cup. We summarize its shape by three biological landmarks on the neural-rim and the fourth landmark as the point of the maximum depth, which is approximately the point where the optic nerve enters this eye cup. These four landmarks are extracted from the images related to some Rhesus monkeys before and after inducing glaucoma. Previous analysis on Bookstein shape coordinates of these four landmarks revealed only marginally significant findings. From clinical experience, it is believed that the ratio depth to diameter of the eye cup provides a useful measure of the shape change. We consider the bootstrap distribution of this normalized 'depth' (G) and give evidence that it provides an appropriate measure of the shape change. This measure G is labelled as the glaucoma index. Further experiments are in progress to validate its use for glaucoma in humans.     

REDUCED DISTANCE MEASURES AND TRANSFORMATIONS IN PROCESSING MULTIVARIATE OUTLIERS

The study of multivariate outliers raises many problems of definition, principle and manipulation. Well-authenticated tests of discordancy exist only for the multivariate normal distribution. Detection of outliers in non-normal distributions involves the adoption of appropriate criteria to represent 'extremeness' of observations in a sample; corresponding tests of discordancy usually require tedious, or even intractable, distributional and computational manipulations. A class of transformations of the data is considered with a view of transferring some of the familiar and desirable features of discordancy tests for normal samples to non-normal situations.     

Outliers in sample surveys

Outliers can as readily arise in sample survey (i.e. finite population) data as in samples from infinite populations. For infinite populations, an extensive methodology exists: very little has been written on the finite population case. We shall explore matters of definition and concept to formulate some basic principles for handling outliers in sample survey data. Some existing methods for outlier accommodation are reviewed and proposals are made for the dual problem of outlier tests of discordancy.     

DETECTION AND TESTING OF DIFFEFENT TYPES OF OUTLIER IN LINEAR STRAUCTURAL RELATIONASHIPS

The linear structural model provides one way of modelling a linear relationship between two random variables. It is well known that problems of unidentifiability arise for unreplicated observations and normal error structure. As in all data sets, outliers can arise and methods are needed for detecting and testing them. An outlier-generating model of mean–slippage type can be used to characterise four different forms of outlier manifestation. It is interesting to find that the unidentifiability problem provides no obstacle for detecting or testing the outliers for three of the four forms. Detection principles, and specific discordancy tests, are derived and illustrated by application to some data on physical measurements of Pacific squid.     

Household size and the poisson distribution

Household size distributions for 104 countries are examined. It is shown that a Poisson distribution truncated at zero can be used to derive models of household size distribution. An improved fit is obtained by adding a linear term to the truncated Poisson model. This distribution depends only on average household size which in turn is shown to be related to modified dependency ratios. This method can be used for comparisons of household size distributions across nations and for long-term forecasting.