Exploiting structure of maximum likelihood estimators for extreme value threshold selection

In order to model the tail of a distribution, one has to define the threshold above or below which an extreme value model produces a suitable fit. Parameter stability plots, whereby one plots maximum likelihood estimates of supposedly threshold-independent parameters against threshold, form one of the main tools for threshold selection by practitioners, principally due to their simplicity. However, one repeated criticism of these plots is their lack of interpretability, with pointwise confidence intervals being strongly dependent across the range of thresholds. In this article, we exploit the independent-increments structure of maximum likelihood estimators in order to produce complementary plots with greater interpretability, and a suggest simple likelihood-based procedure which allows for automated threshold selection

Discussion of "Statistical Modeling of Spatial Extremes" by A. C. Davison, S. A. Padoan and M. Ribatet

Discussion of "Statistical Modeling of Spatial Extremes" by A. C. Davison, S. A. Padoan and M. Ribatet [arXiv:1208.3378].Comment: Published in at http://dx.doi.org/10.1214/12-STS376B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Role of Worker Flows in the Dynamics and Distribution of UK Unemployment

Unemployment varies substantially over time and across subgroups of the labour market. Worker flows among labour market states act as key determinants of this. We examine how the structure of unemployment across groups and its cyclical movements across time are shaped by changes in labour market flows. Using novel estimates of flow transition rates for the UK over the last 35 years, we decompose unemployment variation into parts accounted for by changes in rates of job loss, job finding and flows via non-participation. Close to two-thirds of the volatility of unemployment in the UK over this period can be traced to rises in rates of job loss that accompany recessions. The share of this inflow contribution has been broadly the same in each of the past three recessions. Decreased job-finding rates account for around one-quarter of unemployment cyclicality and the remaining variation can be attributed to flows via non-participation. Digging deeper into the structure of unemployment by gender, age and education, the flow-approach is shown to provide a richer understanding of the unemployment experiences across population subgroups.labour market, unemployment, worker flows

Determining the Dependence Structure of Multivariate Extremes

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take their largest values simultaneously, while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of non-standard cones and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their value through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to UK river flows, estimating the probabilities of different subsets of sites being large simultaneously

The role of worker flows in the dynamics and distribution of UK unemployment

Unemployment varies substantially over time and across subgroups of the labour market. Worker flows among labour market states act as key determinants of this variation. We examine how the structure of unemployment across groups and its cyclical movements across time are shaped by changes in labour market flows. Using novel estimates of flow transition rates for the UK over the last 35 years, we decompose unemployment variation into parts accounted for by changes in rates of job loss, job finding and flows via non-participation. Close to two-thirds of the volatility of unemployment in the UK over this period can be traced to rises in rates of job loss that accompany recessions. The share of this inflow contribution has been broadly the same in each of the past three recessions. Decreased job-finding rates account for around one-quarter of unemployment cyclicality and the remaining variation can be attributed to flows via non-participation. Digging deeper into the structure of unemployment by gender, age and education, the flow-approach is shown to provide a richer understanding of the unemployment experiences across population subgroups. Key words: labour market ; unemployment ; worker flows JEL classification: E24 ; J6

Statistical inference for multivariate extremes via a geometric approach

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, and the geometric approach itself has not been fully exploited for statistical inference. We outline a method for parametric estimation of the limit set shape, which includes a useful non/semi-parametric estimate as a pre-processing step. More fundamentally, our approach provides a new class of asymptotically-motivated statistical models for the tails of multivariate distributions, and such models can accommodate any combination of simultaneous or non-simultaneous extremes through appropriate parametric forms for the limit set shape. Extrapolation further into the tail of the distribution is possible via simulation from the fitted model. A simulation study confirms that our methodology is very competitive with existing approaches, and can successfully allow estimation of small probabilities in regions where other methods struggle. We apply the methodology to two environmental datasets, with diagnostics demonstrating a good fit

The Role of Worker Flows in the Dynamics and Distribution of UK Unemployment

Unemployment varies substantially over time and across subgroups of the labour market. Worker flows among labour market states act as key determinants of this variation. We examine how the structure of unemployment across groups and its cyclical movements across time are shaped by changes in labour market flows. Using novel estimates of flow transition rates for the UK over the last 35 years, we decompose unemployment variation into parts accounted for by changes in rates of job loss, job finding and flows via non-participation. Close to two-thirds of the volatility of unemployment in the UK over this period can be traced to rises in rates of job loss that accompany recessions. The share of this inflow contribution has been broadly the same in each of the past three recessions. Decreased jobfinding rates account for around one-quarter of unemployment cyclicality and the remaining variation can be attributed to flows via non-participation. Digging deeper into the structure of unemployment by gender, age and education, the flow-approach is shown to provide a richer understanding of the unemployment experiences across population subgroups.labour market, unemployment, worker flows

Higher-dimensional spatial extremes via single-site conditioning

Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial extreme value theory based on the conditional multivariate extreme value model, whereby the limit theory is formed through conditioning upon the value at a particular site being extreme. The ensuing methodology allows for a flexible class of dependence structures, as well as models that can be fitted in high dimensions. To overcome issues of conditioning on a single site, we suggest a joint inference scheme based on all observation locations, and implement an importance sampling algorithm to provide spatial realizations and estimates of quantities conditioning upon the process being extreme at any of one of an arbitrary set of locations. The modelling approach is applied to Australian summer temperature extremes, permitting assessment the spatial extent of high temperature events over the continent