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Thesis (Ph. D.)--Rutgers University, 2008. / "Graduate Program in Statistics and Biostatistics." Includes bibliographical references (p. 53-55).

Thesis (Ph. D.)--University of California, San Diego, 2002. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 56-62). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--University of California, San Diego, 2001. / Vita. Includes bibliographical references (leaves 143-146).

Some problems of' statistical inference for discrete-valued time series are investigated in this study. New statistical theories and methods are developed which may aid us in gaining more insight into the understanding of discrete-valued time series data. The first part is concerned with the measurement of the serial dependence of binary time series. In early studies the classical autocorrelation function was used, which, however, may not be an effective and informative means of revealing the dependence feature of a binary time series. Recently, the autopersistence function has been proposed as an alternative to the autocorrelation function for binary time series. The theoretical autopersistence functions and their sample analogues, the autopersistence graphs, are studied within a binary autoregressive model. Some properties of the autopcrsistencc functions and the asymptotic properties of the autopersistence graphs are discussed, justifying that the antopersistence graphs can be used to assess the dependence feature. Besides binary time series, intcger-vall1ed time series arc perhaps the most commonly seen discrete-valued time series. A generalization of the Poisson autoregression model for non-negative integer-valued time series is proposed by imposing an additional threshold structure on the latent mean process of the Poisson autoregression. The geometric ergodicity of the threshold Poisson autoregression with perburbations in the latent mean process and the stochastic stability of the threshold Poisson autoregression are obtained. The maximum likelihood estimator for the parameters is discussed and the conditions for its consistency and asymptotic normally are given as well. Furthermore, there is an increasing need for models of integer-valued time series which can accommodate series with negative observations and dependence structure more complicated than that of an autoregression or a moving average. In this regard, an integer-valued autoregressive moving average process induced by the so-called signed thinning operator is proposed. The first-order model is studied in detail. The conditions for the existence of stationary solution and the existence of finite moments are discussed under general assumptions. Under some further assumptions about the signed thinning operators and the distribution of the innovation, a moment-based estimator for the parameters is proposed, whose consistency and asymptotic normality are also proved. The problem of conducting one-step-ahead forecast is also considered based on hidden Markov chain theory. Simulation studies arc conducted to demonstrate the validity of the theories and methods established above. Real data analysis such as the annual counts of major earthquakes data are also presented to show their potential usefulness in applications. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

No description available.

Eucalypt trees are one of tree species used for the manufacturing of papers in South Africa. The manufacturing of paper consists of cooking the wood with chemicals until obtaining a pulp. The wood is made of different cells. The shape and structure of these cells, called wood anatomical characteristics are important for the quality of paper. In addition, the anatomical characteristics of wood are influenced by environmental factors like climatic factors, soil compositions etc…. In this study we investigated the effects of the climatic factors (temperature, rainfall, solar radiation, relative humidity, and wind speed) on wood anatomical characteristics of two Eucalyptus clones, a GC (Eucalyptus grandis × camuldulensis) and a GU (Eucalyptus grandis × urophylla). Nine trees per clone have been selected. Two sets of data have been collected for this study. The first set of data was eleven anatomical characteristics of the wood formed daily over a period of five years. The second set of data was the daily measurement of temperature, rainfall, solar radiation, relative humidity and wind speed in the experimental area. Wood is made of two kinds of cell, the fibres and the vessels. The fibres are used for the strength and support of the tree and the vessels for the nutrition. Eleven characteristics related to those cells have been measured (diameter, wall thickness, frequency). These characteristics are highly correlated. To reduce the number of response variables, the principal component analysis was used and the first four principal components accounts for about 95% of the total variation. Based on the weights associated with each component the first four principal components were labelled as vessel dimension (VD), fibre dimension (FD), fibre wall (FW) and vessel frequency (VF). The longitudinal linear mixed model with age, season, temperature, rainfall, solar radiation, relative humidity and wind speed as the fixed effects factors and tree as random effect factor was fitted to the data. From time series modelling result, lagged order of climatic variables were identified and these lagged climatic variables were included in the model. To account for the physical characteristic of the trees we included the effect of diameter at breast height, stem radius, daily radial increment, and the suppression or dominance of the tree in the model. It was found that wood anatomical characteristics of the two clones were more affected by climatic variables when the tree was on juvenile stage as compared to mature stage. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

The transmission of malaria is among the leading public health problems in Ethiopia. From the total area of Ethiopia, more than 75% is malarious. Identifying the infectiousness of malaria by socio-economic, demographic and geographic risk factors based on the malaria rapid diagnosis test (RDT) survey results has several advantages for planning, monitoring and controlling, and eventual malaria eradication effort. Such a study requires thorough understanding of the diseases process and associated factors. However such studies are limited. Therefore, the aim of this study was to use different statistical tools suitable to identify socioeconomic, demographic and geographic risk factors of malaria based on the malaria rapid diagnosis test (RDT) survey results in Ethiopia. A total of 224 clusters of about 25 households were selected from the Amhara, Oromiya and Southern Nation Nationalities and People (SNNP) regions of Ethiopia. Accordingly, a number of binary response statistical analysis models were used. Multiple correspondence analysis was carried out to identify the association among socioeconomic, demographic and geographic factors. Moreover a number of binary response models such as survey logistic, GLMM, GLMM with spatial correlation, joint models and semi-parametric models were applied. To test and investigate how well the observed malaria RDT result, use of mosquito nets and use of indoor residual spray data fit the expectations of the model, Rasch model was used. The fitted models have their own strengths and weaknesses. Application of these models was carried out by analysing data on malaria RDT result. The data used in this study, which was conducted from December 2006 to January 2007 by The Carter Center, is from baseline malaria indicator survey in Amhara, Oromiya and Southern Nation Nationalities and People (SNNP) regions of Ethiopia. The correspondence analysis and survey logistic regression model was used to identify predictors which affect malaria RDT results. The effect of identified socioeconomic, demographic and geographic factors were subsequently explored by fitting a generalized linear mixed model (GLMM), i.e., to assess the covariance structures of the random components (to assess the association structure of the data). To examine whether the data displayed any spatial autocorrelation, i.e., whether surveys that are near in space have malaria prevalence or incidence that is similar to the surveys that are far apart, spatial statistics analysis was performed. This was done by introducing spatial autocorrelation structure in GLMM. Moreover, the customary two variables joint modelling approach was extended to three variables joint effect by exploring the joint effect of malaria RDT result, use of mosquito nets and indoor residual spray in the last twelve months. Assessing the association between these outcomes was also of interest. Furthermore, the relationships between the response and some confounding covariates may have unknown functional form. This led to proposing the use of semiparametric additive models which are less restrictive in their specification. Therefore, generalized additive mixed models were used to model the effect of age, family size, number of rooms per person, number of nets per person, altitude and number of months the room sprayed nonparametrically. The result from the study suggests that with the correct use of mosquito nets, indoor residual spraying and other preventative measures, coupled with factors such as the number of rooms in a house, are associated with a decrease in the incidence of malaria as determined by the RDT. However, the study also suggests that the poor are less likely to use these preventative measures to effectively counteract the spread of malaria. In order to determine whether or not the limited number of respondents had undue influence on the malaria RDT result, a Rasch model was used. The result shows that none of the responses had such influences. Therefore, application of the Rasch model has supported the viability of the total sixteen (socio-economic, demographic and geographic) items for measuring malaria RDT result, use of indoor residual spray and use of mosquito nets. From the analysis it can be seen that the scale shows high reliability. Hence, the result from Rasch model supports the analysis carried out in previous models. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2013.

Oftentimes, application of regression models to analyse cereals data is limited to estimating and predicting crop production or yield. The general approach has been to fit the model without much consideration of the problems that accompany application of regression models to real life data, such as collinearity, models not fitting the data correctly and violation of assumptions. These problems may interfere with applicability and usefulness of the models, and compromise validity of results if they are not corrected when fitting the model. We applied regression models and diagnostics on national and household data to model availability of main cereals in Lesotho, namely, maize, sorghum and wheat. The application includes the linear regression model, regression and collinear diagnostics, Box-Cox transformation, ridge regression, quantile regression, logistic regression and its extensions with multiple nominal and ordinal responses. The Linear model with first-order autoregressive process AR(1) was used to determine factors that affected availability of cereals at the national level. Case deletion diagnostics were used to identify extreme observations with influence on different quantities of the fitted regression model, such as estimated parameters, predicted values, and covariance matrix of the estimates. Collinearity diagnostics detected the presence of more than one collinear relationship coexisting in the data set. They also determined variables involved in each relationship, and assessed potential negative impact of collinearity on estimated parameters. Ridge regression remedied collinearity problems by controlling inflation and instability of estimates. The Box-Cox transformation corrected non-constant variance, longer and heavier tails of the distribution of data. These increased applicability and usefulness of the linear models in modeling availability of cereals. Quantile regression, as a robust regression, was applied to the household data as an alternative to classical regression. Classical regression estimates from ordinary least squares method are sensitive to distributions with longer and heavier tails than the normal distribution, as well as to outliers. Quantile regression estimates appear to be more efficient than least squares estimates for a wide range of error term distribution. We studied availability of cereals further by categorizing households according to availability of different cereals, and applied the logistic regression model and its extensions. Logistic regression was applied to model availability and non-availability of cereals. Multinomial logistic regression was applied to model availability with nominal multiple categories. Ordinal logistic regression was applied to model availability with ordinal categories and this made full use of available information. The three variants of logistic regression model gave results that are in agreement, which are also in agreement with the results from the linear regression model and quantile regression model. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.