Mike Heithaus brings a shark next to the boat to be measured, tagged, and sampled, Shark River

This material is based upon work supported by the National Science Foundation through the Florida Coastal Everglades Long-Term Ecological Research program under Cooperative Agreements #DBI-0620409 and #DEB-9910514. This image is made available for non-commercial or educational use only.

Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Changes of Soil Biogeochemistry under Native and Exotic Plants Species

Invasive plant species are major threats to the biodiversity and ecosystem stability. The purpose of this study is to understand the impacts of invasive plants on soil nutrient cycling and ecological functions. Soil samples were collected from rhizosphere and non-rhizosphere of both native and exotic plants from three genera, Lantana, Ficus and Schinus, at Tree Tops Park in South Florida, USA. Experimental results showed that the cultivable bacterial population in the soil under Brazilian pepper (invasive Schinus) was approximately ten times greater than all other plants. Also, Brazilian pepper lived under conditions of significantly lower available phosphorus but higher phosphatase activities than other sampled sites. Moreover, the respiration rates and soil macronutrients in rhizosphere soils of exotic plants were significantly higher than those of the natives (Phosphorus, p=0.034; Total Nitrogen, p=0.0067; Total Carbon, p=0.0243). Overall, the soil biogeochemical status under invasive plants was different from those of the natives.