Abstract
We will discuss the problem of retrospective modeling of case-control data for studying gene- environment interactions in a semiparametric Bayesian framework. The special feature of gene-environment interaction studies is that in many situations it is scientifically plausible to assume that the genetic and environmental factors are independent in the underlying population. Under this additional constraint of gene-environment independence, one can derive more eficient estimation techniques than the traditional prospective logistic regression analysis (Piegorsch et al, 1994; Chatterjee and Carroll, 2005). However, the eficient estimates from the retrospective likelihood may be severely biased under the violation of the independence assumption. Stratification effects present in the population could potentially induce non- independence among genetic factors and environmental exposures. We will first provide a semiparametric Bayesian approach to model stratification effects under the assumption of gene-environment independence. We will then propose an alternative to relax the constraint of gene-environment independence in a natural Bayesian framework to strike a compromise between eficiency and robustness. We will analyze data from a case-control study on ovarian cancer patients conducted in Israel to illustrate our methods. Collabora- tors on material related to the presented work are: Nilanjan Chatterjee (National Cancer Institute), Malay Ghosh (University of Florida), Li Zhang (Cleveland Clinic Foundation) and Samiran Sinha (Texas A & M ).

Abstract
The successful application of Hellinger distance approach to fully parametric models is well known. The corresponding optimal estimators, known as minimum Hellinger distance estimators, are robust and eficient. In this paper, we extend this approach to general semiparametric models. We obtain minimum Hellinger distance and minimumproblem Hellinger distance estimators in this context. The asymptotic properties such as consistency, asymptotic normality, eficiency and adaptivity of the proposed estimators are investigated. The robustness and small sample properties of the proposed estimators are also studied using a Monte Carlo study.

Abstract
The behaviors of young generations (18 to 29 years of age) in Thailand had changed and deviated enormously from the traditional way of the Thai culture and affected the society at large. To learn and understand their lifestyles might lessen the gap between the elders and youngsters, and thus would help lessening the social problems. This survey research aims to study three main aspects of young generations lifestyle; attitudes towards education, attitudes towards the traditional Thai culture and their usage of high technology devices ? computer and mobile phone. By using the questionnaires and face to face interview, the data were collected from four groups of people ? those who were 18 to 21 years, 22 to 25, 26 to 29 and those over 30. The last group gave the pictures of how the adults thought towards the young generations. A total of 1020 young people and 430 older people were included and the survey time spanned from June 2008 to April 2010. By using Descriptive Statistics and the statistical test of difference, it was found that fifty percent of younger groups valued the higher educations and more than half of each young sample group still treasured the old traditional Thai culture. Internet and mobile phone were now parts of their daily lives. However it was found that the three young groups were quite different in spending their money and time on the mobile phone and computer. The adults expected the youngsters to be more helpful to the elders and be more restricted to the traditional culture than they did at present. Should the statistical model about young generations lifestyle be built, the explanation about the ways of young generations behaviors will be clearer and more interesting.

Abstract
Keeping in mind the applications of the flow through porous medium in geophysics, particularly in the study of earths core, importance of viscoelastic fluids in industry and chemical technology and presence of dust/suspended particles in fluids; the hydromagnetic stability of stratified Rivlin-Ericksen fluid saturating a porous medium in the presence of rotation is presented. The stability of the motionless horizontal layer of the fluid having vertical stratifications of the physical parameters; density, viscosity, viscoelasticity, medium porosity, medium permeability, particle number density and magnetic field is considered. After linearizing the relevant hydromagnetic equations, the perturbed quantities are analysed in terms of normal modes. Dispersion relation governing the effects of viscoelasticity, porosity, medium permeability, suspended particles, rotation and magnetic field on the stability of Rivlin-Ericksen fluid is derived. The system is found to be stable for the case of stable stratification as in the case of Newtonian fluids. For the case of unstable stratification, magnetic field succeeds in stabilizing the otherwise unstable system for certain wave number range. The behavior of growth rates with respect to Alfven velocity, medium permeability, suspended particles and angular velocity are found analytically as well as numerically. It has been found that the growth rate decreases with the increase in Alfven velocity and angular velocity; and it increases with the increase in medium permeability and suspended particles.

Abstract
The subject of this work is the study of a value problem describing the quasistatic evolution of semilinear retetype viscoplastic models with internal state variables, and we suppose the problem of Tresca s Friction Law at the presence of recal forces. The existence and uniqueness of the solution is proved using results of evolutionary variational inequalities and a fixed point theorem.

Abstract
In the regression model, we assume that the error terms are independent identically distributed. Furthermore, in case of testing hypothesis on the regression coefficient, we assume that the error terms are normally distributed. However, in time series regression, it is quite likely that the errors are serially correlated. The major consequences of the autocorrelation problem are the Ordinary Least Squares (OLS) estimators still remain unbiased, consistent, but they no longer have the minimum variance. Therefore, the usual t and F tests are not generally reliable. An alternative to this traditional is to use a permutation test. Permutation test was applied for linear model in many fields but rarely in time series regression. In this article we proposed permutation test for testing partial regression coefficient for time series with first-order autocorrelation(AR1) where the distribution of error terms is not necessary normal. The Prais-Winsten transformation was applied so that errors are i.i.d. and then exchangeability are also obtained. In addition, we proposed a permutation method that can be directly conducted to the test without fitting back to the model which is not the same as the others well-known permutations test, e.g., Freedman and Lane (1983) and Manly (1997). The asymptotic distribution of the proposed test is also considered. The type I error rate and power of the proposed method and the others permutation methods are studied using numerical simulation.