Some Aspects of Smoothing Techniques in the Moelling of Spatial Data

Diblasi, Angela Magdalena (1996) Some Aspects of Smoothing Techniques in the Moelling of Spatial Data. PhD thesis, University of Glasgow.

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Abstract

The purpose of this thesis is to explore, apply and develop statistical tools in the area which has been called Spatial Statistics. Through all of this work, a key link is the use of smoothers. Specifically, loess and splines are used in the second chapter and kernel smoothers in the rest. Smoothing techniques are now widely used in a variety of modelling problems. It is their application to the specific area of spatial statistics which is the focus of this thesis. One particular application involves the modelling the mackerel egg density in the eastern Atlantic This led to the proposal of a generalized additive model for these data. Due to lack of distributional theory for estimators and methods of selection of a model, the proposed model is the result of an analysis which is analogous to that used in the context of generalized linear models. To assess and compare this model with others proposed in the literature, from the point of view of the estimation of the total number of mackerel eggs, the technique of the bootstrap is used. The spatial processes considered in each chapter are of the form: Y(si) = f(x(si))+epsilon(si), i = l,...,n where x = (x1,x2,..., xm) is a vector of covariates and Si, i = 1,..., n are the locations where the process{Y(s) : s ∈ D}is observed, and epsilon(si), i = 1,... ,n is the process of errors at the observed locations which is assumed gaussian, stationary and isotropic through the whole work. Checking the covariance structure of this kind of spatial processes led to the development of a test statistic for the null hypothesis of constant variogram. Because of the lack of distributional theory for the residuals of a generalized additive model, the test is proposed for the case where the function f of the covariates is a linear function. A test for checking homoscedasticity in a linear model is also proposed as a preliminary study of that for the constant variogram. In both cases, reference bands are also proposed as graphical tools to check constant variance and constant variogram, respectively. The block-bootstrap approach is analyzed to build confidence intervals for the variogram when it is generated from a regular grid in R2. The percentage coverage of these intervals is compared with a technique proposed in the literature under more restrictive assumptions. Techniques of resampling and simulation are employed through the whole work, and the available methods in this area are reviewed and compared as a separate exercise. Further suggestions are also made.

Item Type: Thesis (PhD) Doctoral Adviser: Adrian Bowan Statistics 1996 Enlighten Team glathesis:1996-76472 Copyright of this thesis is held by the author. 19 Nov 2019 14:18 19 Nov 2019 14:18 http://theses.gla.ac.uk/id/eprint/76472