Aspects of robust linear regression

Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that $S$-estimators satisfy an exact Holder condition of order 1/2 at models with normal errors. In Section 5 the breakdown points of the Hampel-Krasker dispersion and regression functionals are shown to be 0. The exact breakdown point of the Krasker-Welsch dispersion functional is obtained as well as bounds for the corresponding regression functional. Section 6 contains the construction of a linearly equivariant, high breakdown and locally Lipschitz dispersion functional for any design distribution. In Section 7 it is shown that there is no inherent contradiction between efficiency and a high breakdown point. Section 8 contains a linearly equivariant, high breakdown regression functional which is Lipschitz continuous at models with normal errors

Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices

It is shown under appropriate conditions that Rousseeuw's minimum volume estimator and other $S$-estimators of multivariate location and dispersion parameters are consistent. Under certain differentiability conditions the estimates are asymptotically normally distributed with a norming factor of $n^{1/2}$

The asymptotics of Rousseeuw's minimum volume ellipsoid estimator

Rousseeuw's minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator. In this paper we establish that it satisfies a local Holder condition of order $1/2$ and converges weakly at the rate of $n^{-1/3}$ to a non-Gaussian distribution

Local Hölder conditions for the local times of certain stationary Gaussian processes

A local Holder condition is obtained for the local time of a stationary Gaussian process with spectral density function proportional to $(a^2 + \lambda^2)^{-(\alpha +\frac{1}{2})}$. A lower bound for the Hausdorff measure of the zero set of the process is also obtained

Method for rating power cables buried in surface troughs

An alternative method is detailed by which the ambient temperature parameter as applied to the calculation of ratings of cables buried in surface trough installations can be determined. Improvement in the accuracy of cable rating calculations will allow greater utilisation of the cable asset and assist for example in the planning of system outages for maintenance work. The proposed model calculates the temperature at the cable burial depth based on measurements of solar radiation, windspeed and air temperature. The model is based on physical laws rather than empirical approaches that have been shown to be generally conservative in application. Results based on weather data monitored over a two-year period show that the ambient temperature of the soil at cable depth can be accurately determined and the model provides a significant improvement on existing methods

Condition monitoring and prognostic indicators for network reliability

Large-scale investment in transmission and distribution networks are planned over the next 10-15 years to meet future demand and changes in power generation. However, it is important that existing assets continue to operate reliably and their health maintained. A research project is considering the increased use of simulation models that could provide accurate prognostics, targeting maintenance and reduce in service failures. Such models could be further refined with parameters obtained from on-line measurements at the asset. It is also important to consider the future development of the research agenda for condition monitoring of power networks and with colleagues from National Grid, PPA Energy and the Universities of Manchester and Strathclyde, the research team are preparing a Position Paper on this subject

Asymptotics for the minimum covariance determinant estimator

Consistency is shown for the minimum covariance determinant (MCD) estimators of multivariate location and scale and asymptotic normality is shown for the former. The proofs are made possible by showing a separating ellipsoid property for the MCD subset of observations. An analogous property is shown for the MCD subset computed from the population distribution

Molecular epidemiology and transmission dynamics of S.uberis bovine clinical mastitis

Mastitis remains one of the most common, costly and intractable diseases affecting the dairy cattle industry worldwide. In spite of concerted efforts meaningful progress in reducing the incidence of mastitis has been limited over the past thirty years by our partial understanding of the epidemiology of key pathogens, such as S.uberis. The aim of this thesis was to investigate the epidemiology of S.uberis mastitis by analysis of the population structure and transmission dynamics of clinical mastitis patterns within and between commercial dairy herds in England and Wales. In Chapter 3 Multi Locus Sequence Typing (MLST) was used to describe the sub-species (sequence type) genetic heterogeneity of S.uberis isolates collected from a longitudinal study of clinical mastitis on 52 farms. The clinical cases were classified according the pattern of occurrence of the sequence types in the herds. The findings suggested that a small subset of MLST sequence types were disproportionally important in the epidemiology of S.uberis mastitis, with cow-to-cow transmission of S.uberis, potentially occurring in the majority of herds in the United Kingdom; this may be the most important route of S.uberis transmission in approximately one third of herds. In Chapter 4 cow and herd level variables, including monthly recorded milk constituents, yield and parity were evaluated against the clinical case classifications defined in Chapter 3. The temporal relationships between clinical cases and classifications were also evaluated as potential predictors of transmission dynamics within a herd. The findings indicated that the time interval between clinical cases classified by genotype as potentially contagious transmission was significantly shorter than that between successive mastitis clinical cases attributed to environmental transmission. The distribution of clinical cases throughout lactation also indicated a higher proportion of potentially contagious isolates were cultured from clinical cases originating from lactation rather than the dry period compared to those attributed to environmental transmission. In Chapter 5 Matrix Assisted Laser Desorption (MALDI) mass spectroscopy was used to generate spectral profiles of S.uberis isolates cellular composition. Spectral profiles were used successfully as an alternative method of discriminating between clinical mastitis isolates associated with contagious transmission from those associated with and environmental origin of infection defined in Chapter 3. The findings of this chapter demonstrated marked variation between herds in the spectral profiles of isolates from the same clinical case classification. In Chapter 6 selected isolates of S.uberis associated with contagious transmission and persistent intramammary infections were sequenced using next generation technology and compared by core genome multi locus sequence typing (cgMLST) to evaluate the discriminatory capacity of the MLST and MALDI. The results from this chapter confirmed the importance of the herd unit in the genotypic population structure of S.uberis suggested by the results of Chapter 5 and also support the results of Chapter3 which suggest ‘low grade’ contagious transmission of S.uberis is superimposed on a ubiquitous, environmental S.uberis mastitis pattern in many herds This thesis demonstrated that the S.uberis population is complex with variation at the bacterial, cow and herd level suggesting different patterns of disease and bacterial evolution occurring in different circumstances. Categorisation of sub-species of S.uberis within herds as being transmitted via contagious or environmental routes appears to be eminently achievable using modern, high throughput technologies; this could lead to a step change in mastitis control