Minimum Hellinger distance (MHDE) estimation is obtained by minimizing the Hellinger distance between an assumed parametric model and a nonparametric estimation of the model. This estimation receives increasing attention over the past decades due to its asymptotic efficiency and excellent robustness against small deviations from assumed model. Minimum profile Hellinger dis- tance (MPHDE) estimation, proposed by Wu and Karunamuni (2015), is an extension of MHDE particularly for semiparametric models. In this thesis, we investigate two-sample symmetric loca- tion models and propose to use MPHDE to estimate the unknown location parameters. Asymptotic normality and robustness properties of the estimation are discussed and a comparison with LSE and MLE is carried out through Monte Carlo simulation studies. The results show that MPHDE is very competitive with LSE and MLE in terms of efficiency , while it appears to be much more robust than LSE and MLE against outlying observations. We also demonstrate the application of the estimation to a breast cancer data.