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Title: On polynomial expansions in modelling and smoothing transect data
Author: Heatley, P.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 1999
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The focus of this study is the modelling and smoothing of transect data. The former requires parameter estimation in statistical models for data with spatial dependence or correlation, while the latter requires the study of penalty functions specifying the degree of smoothing required. Both aspects typically involve the computation of determinants and inverses of matrices, and such calculations are computationally expensive if reliable estimation of parameters is required. This investigation addresses such practical difficulties by developing computationally efficient and robust frameworks for parameter estimation for models in these related fields of study. For the first, we consider the estimation of correlation and related parameters using the likelihoods of the spatial linear model. Here, spatial observations are regarded as dependent observations in d-dimensional space, with special emphasis on d=1. The correlation structure is assumed to be of known functional form, depending on a finite number of parameters and the relative locations of the data points. Thus, for particular correlation functions and sampling configurations, it is possible to express quantities in likelihood functions as polynomials in the parameters of the correlation function. This facilitates efficient estimation of parameters and therefore permits a comprehensive examination of likelihood functions. As it is well-known that these functions can, in certain circumstances, be seriously multimodal, our results have both theoretical and practical interest, by providing useful assessments of the behaviour the likelihoods, in conjunction with details on the application of the computationally efficient polynomial based estimation framework. The second area for discussion involves the application of the polynomial framework in the estimation of parameters in difference-based methodologies for the smoothing of transect data. The polynomial framework leads to useful formulae for quantities in penalty functions, leading to the selection of a smoothing parameter. Then, by numerical examination, we assess the consistency in the degree of smoothing prescribed by various criteria, again data which exhibits some spatial dependence.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available