In this study, the most prominent goodness-of-fit tests for censored samples are reviewed. Power properties of goodness-of-fit statistics of the null hypothesis that a sample which is censored from right, left and both right and left which comes from uniform, normal and exponential distributions are investigated. Then, by a similar argument extreme value, student t with 6 degrees of freedom and generalized logistic distributions are discussed in detail through a comprehensive simulation study. A variety of real life applications are given. Suitable test statistics for testing the above distributions for censored samples are also suggested in the conclusion.

Epidemiological data with disease characteristic information can be modelled in several ways. One way is taking each disease characteristic as a response and constructing binary or polytomous logistic regression model. Second way is using a new response which consists of disease subtypes created by cross-classification of disease characteristic levels, and then constructing polytomous logistic regression model. The former may be disadvantageous since any possible covariation between disease characteristics is neglected, whereas the latter can capture that covariation behaviour. However, cross-classifying the characteristic levels increases the number of categories of response, so that dimensionality problem in parameter space may occur in classical polytomous logistic regression model. A two staged polytomous logistic regression model overcomes that dimensionality problem. In this thesis, study is progressen in two main directions: simulation study and data analysis parts. In simulation study, models that capture the covariation behaviour are compared in terms of the response model parameter estimators. That is, performances of the maximum likelihood estimation (MLE) approach to classical polytomous logistic regression, Bayesian estimation approach to classical polytomous logistic regression and pseudo-conditional likelihood (PCL) estimation approach to two stage polytomous logistic regression are compared in terms of bias and variation of estimators. Results of the simulation study revealed that for small sized sample and small number of disease subtypes, PCL outperforms in terms of bias and variance. For medium scaled size of total disease subtypes situation when sample size is small, PCL performs better than MLE, however when the sample size gets larger MLE has better performance in terms of standard errors of estimates. In addition, sampling variance of PCL estimators of two stage model converges to asymptotic variance faster than the ML estimators of classical polytomous logistic regression model. In data analysis, etiologic heterogeneity in breast cancer subtypes of Turkish female cancer patients is investigated, and the superiority of the two stage polytomous logistic regression model over the classical polytomous logistic model with disease subtypes is represented in terms of the interpretation of parameters and convenience in hypothesis testing.

Bootstrapping is a resampling technique which treats the original data set as a population and draws samples from it with replacement. This technique is widely used, especially, in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, Conic Multivariate Adaptive Regression Splines (CMARS). Here, the CMARS method, which uses conic quadratic optimization, is a modified version of a well-known nonparametric regression model, Multivariate Adaptive Regression Splines (MARS). Although performing better with respect to several criteria, the CMARS model is more complex than that of MARS. To overcome this problem, and to improve the CMARS performance further, three different bootstrapping regression methods, namely, Random-X, Fixed-X and Wild Bootstrap are applied on four data sets with different size and scale. Then, the performances of the models are compared using various criteria including accuracy, precision, complexity, stability, robustness and efficiency. Random-X yields more precise, accurate and less complex models particularly for medium size and medium scale data even though it is the least efficient method.

ABSTRACT ROBUST CONTROL CHARTS &Ccedil / etiny&uuml / rek, Aysun M. Sc., Department of Statistics Supervisor: Dr. BariS S&uuml / r&uuml / c&uuml / Co-Supervisor: Assoc. Prof. Dr. Birdal Senoglu December 2006, 82 pages Control charts are one of the most commonly used tools in statistical process control. A prominent feature of the statistical process control is the Shewhart control chart that depends on the assumption of normality. However, violations of underlying normality assumption are common in practice. For this reason, control charts for symmetric distributions for both long- and short-tailed distributions are constructed by using least squares estimators and the robust estimators -modified maximum likelihood, trim, MAD and wave. In order to evaluate the performance of the charts under the assumed distribution and investigate robustness properties, the probability of plotting outside the control limits is calculated via Monte Carlo simulation technique.

The longitudinal feature of measurements and counting process of responses motivate the regression models for longitudinal count data (LCD) to take into account the phenomenons such as within-subject association and overdispersion. One common problem in longitudinal studies is the missing data problem, which adds additional difficulties into the analysis. The missingness can be handled with missing data techniques. However, the amount of missingness in the data and the missingness mechanism that the data have affect the performance of missing data techniques. In this thesis, among the regression models for LCD, the Log-Log-Gamma marginalized multilevel model (Log-Log-Gamma MMM) and the random-intercept model are focused on. The performance of the models is compared via a simulation study under three missing data mechanisms (missing completely at random, missing at random conditional on observed data, and missing not random), two types of missingness percentage (10% and 20%), and four missing data techniques (complete case analysis, subject, occasion and conditional mean imputation). The simulation study shows that while the mean absolute error and mean square error values of Log-Log-Gamma MMM are larger in amount compared to the random-intercept model, both regression models yield parallel results. The simulation study results justify that the amount of missingness in the data and that the missingness mechanism that the data have, strictly influence the performance of missing data techniques under both regression models. Furthermore, while generally occasion mean imputation displays the worst performance, conditional mean imputation shows a superior performance over occasion and subject mean imputation and gives parallel results with complete case analysis.

Conditional Cash Transfer (CCT) is a social assistance program which aims for investing in human capital by enabling families under risk of poverty to send their children to school and to benefit from health services regularly. CCT aims for decreasing poverty by means of cash transfers in the short run and aims for investing in children&rsquo / s human capital by providing basic preventative health care, regular school attendance and nutrition in the long run. Under the state of these aims, beginning from 1990s, more than 20 countries in the world started their own CCT program by the mediation or leadership of World Bank. CCT program in Turkey started so as to decrease the adverse effects of economic crisis in 2001 within the Social Risk Mitigation Project which was financially supported by the World Bank loan and constituted under the Social Assistance and Solidarity Foundation. CCT program in Turkey has been adopted by poor families in recent years, and demands and overall payments within the program have been increased significantly in a consideration of years. The need for examining and predicting the increase in these demands scientifically / and considering the fact that CCT is being applied over 20 countries, and such a study being never done before made this study necessary. In this thesis study, the change of CCT applications and number of beneficiary household over time were modeled using multivariate time series models according to geographical regions. Using the vector autoregressive models with exogenous variables (VARX), the forecasts were obtained for the number of CCT applications and beneficiary households in the future.

Health problems of the human beings in a society are one of the main components of the social security systems due to the dimension of the financial burden it might bring on individuals, employers, insurance companies and governments. Morbidity measures, such as incidence and prevalence of a specific disease in a certain population enable researchers to estimate for individuals the probability of being diagnosed or being prone to the diseases. This information is usually not tractable because of the non-availability of the convenient data or recordings for many countries as well as Turkey. Even if it is available, it is commonly limited with largely varying characteristics about the type and coverage of the diseases. In this regard, the pattern that a population follows for an acute disease may not be the same for chronic diseases. Having those indicators determined for a group of insureds will enable underwriters to have more profitable and economical premium calculation and precision on required reserve estimation. v Based on their characteristics such as acute or chronic behaviour, the gender, and the location of residency of people, the diseases show different behaviour on their occurrences. From the insurer