It is standard practice to assume the discounted utility (DU) model on the part of the economic agents. This thesis tests the key axiom of the DU model (stationarity) in the health domain. Intertemporal preferences for health are of interest because of the debate over the appropriate treatment of future health effects in economic evaluation and of the relationship between intertemporal preferences and health-affecting behaviour. Social intertemporal preferences for fatal changes in health and private and social intertemporal preferences for non-fatal changes were elicited from members of the general public. Private intertemporal preferences for non-fatal changes were elicited from university students. Stationarity was violated in all three studies indicating that the DU model does not accurately describe individuals' intertemporal preferences. Psychologists dissatisfied with the DU model have developed hyperbolic models which replace the stationarity axiom by a generalised stationarity axiom. This thesis compared the descriptive properties of the DU model and hyperbolic discounting models in the health domain. The results showed that the hyperbolic discounting models fitted the data better than the DU model. This indicates that hyperbolic models should be preferred in the analyses of health affecting behaviour. Whether they should also be used in economic evaluations is likely to depend on other criteria as well as descriptive superiority. To inform the debate about the appropriate discount rate for health effects in economic evaluations this thesis investigated whether intertemporal preferences differ across outcomes within the health domain. The results showed that private and social intertemporal preferences for non-fatal changes in health are very similar. More differences were found between intertemporal preferences for fatal changes and non-fatal changes. This indicates that the debate over the relationship between individuals' preferences and the social discount rate is less important and that the debate should perhaps focus more on whether the rate should depend on the type of health outcome of the intervention.

Medium and short term mine planning require models of mineral deposits that account for internal geological structures that permit scheduling of mine production at a weekly and monthly production periods. Modified kriging estimation techniques are used for accounting for such geologic structures. However, in the case of simulation, it is strongly linked to the use of sequential Gaussian simulation which has difficulties in reproducing internal geologic patterns. This thesis presents: (1) a set of tools to verify the impact of mean and variance trends in a domain; (2) a methodology for identifying highly variable sub-regions within domains; and (3) a simulation methodology that accounts for the internal structures in the domain required by medium and short term planning. Specifically, the simulation approach consists of: (1) moving the domain to a high dimensional space where the features of the internal structures in the domain are more stationary, (2) simulating the realizations via sequential Gaussian simulation, and (3) projecting the results to the initial dimensional space. / Mining Engineering

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<p>The objective of this study is to develop a multiple linear regression model that measures the relationship between the church services supply and the attendance to the services in the Uppsala diocese, Church of Sweden. By reviewing previous models and examining the nature of data available, two research questions were introduced, namely, the problem of omitted variables and the problem of spatial autocorrelation. For the first question, two methods were compared, namely, the Y-lag method and the first-differenced equation. Statistical tests then showed that the latter was more preferable for this study. For the second question, geographically weighted regression was used to examine the spatial variations in relationships estimated by above modeling strategies. However, no significant spatial variation was found for them. In conclusion, by using the ordinary least square estimation for the first-differenced equation the most suitable regression model was obtained. The data showed no need to consider the issue of spatial non-stationarity.</p>

The objective of this study is to develop a multiple linear regression model that measures the relationship between the church services supply and the attendance to the services in the Uppsala diocese, Church of Sweden. By reviewing previous models and examining the nature of data available, two research questions were introduced, namely, the problem of omitted variables and the problem of spatial autocorrelation. For the first question, two methods were compared, namely, the Y-lag method and the first-differenced equation. Statistical tests then showed that the latter was more preferable for this study. For the second question, geographically weighted regression was used to examine the spatial variations in relationships estimated by above modeling strategies. However, no significant spatial variation was found for them. In conclusion, by using the ordinary least square estimation for the first-differenced equation the most suitable regression model was obtained. The data showed no need to consider the issue of spatial non-stationarity.

This study estimates cointegration models by applying the Engle-Granger (1989) two-step es- timation procedure, the Phillip-Ouliaris (1990) residual-based test and Johansen's multivariate technique. The cointegration techniques are tested on the Raotbl3 data set, the World Economic Indicators data set and the UKpppuip data set using statistical software R. In the Raotbl3 data set, we test for cointegration between the consumption expenditure, and income and wealth vari- ables. In the world economic indicators data set, we test for cointegration in three of Australia's key economic indicators, whereas in the UKpppuip data set we test for the existence of long-run economic relationships in the United Kingdom's purchasing power parity. The study nds the three techniques not to be consistent, that is, they do not lead to the same results. However, it recommends the use of Johansen's method because it is able to detect more than one cointegrating relationship if present.

Faculty of Science School of Statistics snd Acturial Science 9907894x craig.morgan@goldfields.co.za / This dissertation presents a detailed study of geostatistics. Included in this work are details of the development of geostatistics and its usefulness both in and outside of the mining industry, a comprehensive presentation of the theory of geostatistics, and a discussion of the application of this theory to practical situations. A published debate over the validity of geostatistics is also examined. The ultimate goal of this dissertation is to provide a thorough investigation of geostatistics from both a theoretical and a practical perspective. The theory presented in this dissertation is thus tested on various spatial data sets, and from these tests it is concluded that geostatistics can be effectively used in practice provided that the practitioner fully understands the theory of geostatistics and the spatial data being analyzed. A particularly interesting conclusion to come out of this dissertation is the importance of using additive regionalized variables in all geostatistical analyses.

Linear factor models have attracted considerable interest over recent years especially in the econometrics literature. The intuitively appealing idea to explain a panel of economic variables by a few common factors is one of the reasons for their popularity. From a statistical viewpoint, the need to reduce the cross-section dimension to a much smaller factor space dimension is obvious considering the large data sets available in economics and finance. One of the characteristics of the traditional factor model is that the process is stationary in the time dimension. This appears restrictive, given the fact that over long time periods it is unlikely that e.g. factor loadings remain constant. For example, in the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), typical empirical results show that factor loadings are time-varying, which in the CAPM is caused by time-varying second moments. In this thesis we generalize the tools of factor analysis for the study of stochastic processes whose behavior evolves over time. In particular, we introduce a new class of factor models with loadings that are allowed to be smooth functions of time. To estimate the resulting nonstationary factor model we generalize the properties of the principal components technique to the time-varying framework. We mainly consider separately two classes of Evolutionary Factor Models: Evolutionary Static Factor Models (Chapter 2) and Evolutionary Dynamic Factor Models (Chapter 3). In Chapter 2 we propose a new approximate factor model where the common components are static but nonstationary. The nonstationarity is introduced by the time-varying factor loadings, that are estimated by the eigenvectors of a nonparametrically estimated covariance matrix. Under simultaneous asymptotics (cross-section and time dimension go to infinity simultaneously), we give conditions for consistency of our estimators of the time varying covariance matrix, the loadings and the factors. This paper generalizes to the locally stationary case the results given by Bai (2003) in the stationary framework. A simulation study illustrates the performance of these estimators. The estimators proposed in Chapter 2 are based on a nonparametric estimator of the covariance matrix whose entries are computed with the same moothing parameter. This approach has the advantage of guaranteeing a positive definite estimator but it does not adapt to the different degree of smoothness of the different entries of the covariance matrix. In Chapter 5 we give an additional theoretical result which explains how to construct a positive definite estimate of the covariance matrix while while permitting different smoothing parameters. This estimator is based on the Cholesky decomposition of a pre-estimator of the covariance matrix. In Chapter 3 we introduce the dynamics in our modeling. This model generalizes the dynamic (but stationary) factor model of Forni et al. (2000), as well as the nonstationary (but static) factor model of Chapter 2. In the stationary (dynamic) case, Forni et al. (2000) show that the common components are estimated by the eigenvectors of a consistent estimator of the spectral density matrix, which is a matrix depending only on the frequency. In the evolutionary framework the dynamics of the model is explained by a time-varying spectral density matrix. This operator is a function of time as well as of the frequency. In this chapter we show that the common components of a locally stationary dynamic factor model can be estimated consistently by the eigenvectors of a consistent estimator of the time-varying spectral density matrix. In Chapter 4 we apply our theoretical results to real data and compare the performance of our approach with that based on standard techniques. Chapter 6 concludes and mention the main questions for future research.

This study estimates cointegration models by applying the Engle-Granger (1989) two-step es- timation procedure, the Phillip-Ouliaris (1990) residual-based test and Johansen's multivariate technique. The cointegration techniques are tested on the Raotbl3 data set, the World Economic Indicators data set and the UKpppuip data set using statistical software R. In the Raotbl3 data set, we test for cointegration between the consumption expenditure, and income and wealth vari- ables. In the world economic indicators data set, we test for cointegration in three of Australia's key economic indicators, whereas in the UKpppuip data set we test for the existence of long-run economic relationships in the United Kingdom's purchasing power parity. The study nds the three techniques not to be consistent, that is, they do not lead to the same results. However, it recommends the use of Johansen's method because it is able to detect more than one cointegrating relationship if present. / Decision Sciences / M. Com. (Statistics)

In this dissertation, we utilize the discrete Fourier analysis on axially symmetric data generation and nonparametric estimation. We first represent the axially symmetric process as Fourier series on circles with the Fourier random coefficients expressed as circularlysymmetric complex random vectors. We develop an algorithm to generate the axially symmetric data that follow the given covariance function. Our simulation study demonstrates that our approach performs comparable with the classical approach using the given axially symmetric covariance function directly, while at the same time significantly reducing computational costs. For the second contribution of this dissertation, we apply the discrete Fourier transform to provide the nonparametric estimation on the covariance function of the above circularly-symmetric complex random vectors under gridded data structure. Our results show that these estimates has closely related to the simultaneous diagonalization of circulant matrices. The simulation study shows that our proposed estimates match well with their theoretical counterparts. Finally through the Fourier transform of the original gridded data, the covariance estimator of an axially symmetric process based on the method of moments can be represented as a quadratic form of transformed data that is associated with a rotation matrix.