Browsing by Author "Thiart, Christien"
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- ItemOpen AccessAspects of estimation in the linear model with special reference to collinearity(1994) Thiart, Christien; Dunne, Tim; Troskie, Cas
- ItemOpen AccessCollinearity and consequences for estimation: a study and simulation(1990) Thiart, Christien; Dunne, T T
- ItemOpen AccessComparison of ridge and other shrinkage estimation techniques(2006) Vumbukani, Bokang C; Thiart, ChristienShrinkage estimation is an increasingly popular class of biased parameter estimation techniques, vital when the columns of the matrix of independent variables X exhibit dependencies or near dependencies. These dependencies often lead to serious problems in least squares estimation: inflated variances and mean squared errors of estimates unstable coefficients, imprecision and improper estimation. Shrinkage methods allow for a little bias and at the same time introduce smaller mean squared error and variances for the biased estimators, compared to those of unbiased estimators. However, shrinkage methods are based on the shrinkage factor, of which estimation depends on the unknown values, often computed from the OLS solution. We argue that the instability of OLS estimates may have an adverse effect on performance of shrinkage estimators. Hence a new method for estimating the shrinkage factors is proposed and applied on ridge and generalized ridge regression. We propose that the new shrinkage factors should be based on the principal components instead of the unstable OLS estimates.
- ItemOpen AccessContributions to spatial uncertainty modelling in GIS : small sample data(2007) Guo, Danni; Thiart, ChristienEnvironmental data is very costly and difficult to collect and are often vague (subjective) or imprecise in nature (e.g. hazard level of pollutants are classified as "harmful for human beings"). These realities in practise (fuzziness and small datasets) leads to uncertainty, which is addressed by my research objective: "To model spatial environmental data with .fuzzy uncertainty, and to explore the use of small sample data in spatial modelling predictions, within Geographic Information System (GIS)." The methodologies underlying the theoretical foundations for spatial modelling are examined, such as geostatistics, fuzzy mathematics Grey System Theory, and (V,·) Credibility Measure Theory. Fifteen papers including three journal papers were written in contribution to the developments of spatial fuzzy and grey uncertainty modelling, in which I have a contributed portion of 50 to 65%. The methods and theories have been merged together in these papers, and they are applied to two datasets, PM10 air pollution data and soil dioxin data. The papers can be classified into two broad categories: fuzzy spatial GIS modelling and grey spatial GIS modelling. In fuzzy spatial GIS modelling, the fuzzy uncertainty (Zadeh, 1965) in environmental data is addressed. The thesis developed a fuzzy membership grades kriging approach by converting fuzzy subsets spatial modelling into membership grade spatial modelling. As this method develops, the fuzzy membership grades kriging is put into the foundation of the credibility measure theory, and approached a full data-assimilated membership function in terms of maximum fuzzy entropy principle. The variable modelling method in dealing with fuzzy data is a unique contribution to the fuzzy spatial GIS modelling literature. In grey spatial GIS modelling, spatial predictions using small sample data is addressed. The thesis developed a Grey GIS modelling approach, and two-dimensional order-less spatially observations are converted into two one-dimensional ordered data sequences. The thesis papers also explored foundational problems within the grey differential equation models (Deng, 1985). It is discovered the coupling feature of grey differential equations together with the help of e-similarity measure, generalise the classical GM( 1,1) model into more classes of extended GM( 1,1) models, in order to fully assimilate with sample data information. The development of grey spatial GIS modelling is a creative contribution to handling small sample data.
- ItemOpen AccessGeographically weighted regression and an extension(2008) Miller, Karen M; Haines, Linda; Thiart, ChristienIncludes abstract. Includes bibliographical references (leaves [72]-75).
- ItemOpen AccessInvestigating 'optimal' kriging variance estimation :analytic and bootstrap estimators(2011) Ngwenya, Mzabalazo Z; Thiart, Christien; Haines, LindaKriging is a widely used group of techniques for predicting unobserved responses at specified locations using a set of observations obtained from known locations. Kriging predictors are best linear unbiased predictors (BLUPs) and the precision of predictions obtained from them are assessed by the mean squared prediction error (MSPE), commonly termed the kriging variance.
- ItemOpen AccessQuantifying spatial association between mineral deposits and geology across three African crustal segments of different age, with implication for secular change in mineralization during earth history(2006) Mabidi, Tshifhiwa; De Wit, Maarten; Thiart, ChristienVariations in enrichment of mineralization, expressed in ore deposits, in the continental crust may be one way to test for secular changes in crustal genesis. This study collates and analyses fundamental information about mineral deposits with which to 'fingerprint' the metal endowment of African crust of different age. Three areas of juvenile African crust (e.g. mantle derived over similar lengths of time of ~500 million years, and excluding recycled older crust) of different ages with similar geology are compared. The areas range in age from 0.5 to 3.0 Ga, [e.g. the Zimbabwe Craton (2.5-3.0 Ga), the Birimian Shield (1.8-2.3 Ga), and the Arabian-Nubian Shield (0.5-1.0 Ga)]. The three areas have a total of 2671 mineral deposits, which are divided into six groups according to their geochemical affinities. Using these known deposits, mineral potential maps are created through a data driven approach, using weights of evidence (WotE). The layers/themes used in Woffi are (1) lithology, (2) structures (faults and shear zones), and (3) lithological contacts. The analysis shows that there is strong lithology control on mineralization in all three areas. Archean crust has high predictive values compared to the younger crust. A measure of spatial association (spatial coefficient), based on the WotE approach, is also used to 'fingerprint' the met I endowment in the three selected regions of African crust. The patterns of the mineral deposits distribution within all regions shows that each region has a unique metal endowment, and that there is a greater concentration of mineral deposits in the crust of the Archean Zimbabwe Craton relative to the younger crust of the Birimian and Arabian-Nubian Shields. The analysis of this study therefore quantitatively corroborates studies that suggest older crust is more mineral diverse and more enriched in mineral deposits than younger crust. Thus, secular changes in mineralization or rates of tectonic processes, or both, are implicated, and mineral endowment in the African crust has undergone major evolutionary changes from Archean to Neoproterozoic time.
- ItemOpen AccessVariable modeling of spatially distributed random interval observation(2007) Wabiri, Njeri; Thiart, Christien; Guo, RenkuanIncludes bibliographical references.