This research will extend existing parametric and nonparametric regression methods. Regression analysis is widely used on data to determine relationship of two or more variables of interest. New methods need to be invented to take in to account various characters of the data. The research will study biased estimators of parameters in a partial spline model. This model can be used to compare two or more populations. The investigator will also look at test statistic to compare "mean curves" with or without the help of the covariates.