Browsing by Author "Li, Jiang"

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    Minimum Profile Hellinger Distance Estimation for Semiparametric Simple Linear Regression Model
    (2021-01-06) Li, Jiang; Wu, Jingjing; Li, Haocheng; Wu, Jingjing; Li, Haocheng; Lu, Xuewen; Zhang, Qingrun
    The simple linear regression model is essential for analyzing the relation between a response variable and a covariate variable, and the importance of simple linear regression model for statistical analysis of data is well documented. This thesis focuses on the semiparametric simple linear regression model where the distribution of the error term is assumed symmetric but otherwise completely unspecified. Under this model, we constructed a robust estimator of the regression coefficient parameters using the minimum Hellinger distance technique. Minimum Hellinger Distance Estimation (MHDE) was first introduced by Beran (1977) for fully parametric models that has been shown to have good efficiency and robustness properties. In the past decade, the MHDE has been extended to semiparametric models. Furthermore, Wu and Karunamuni (2015) introduced the Minimum Profile Hellinger Distance Estimation (MPHDE) for semeparametric models which retains good efficiency and robustness properties of MHDE in parametric models. In this thesis, I constructed an MPHDE for the semiparametric simple linear regression model. We established in theory the consistency of the proposed MPHDE. Finite-sample performance of the proposed estimator was examined via simulation studies and real data applications. Our numerical results showed that the proposed MPHDE has good efficiency and simultaneously is very robust against outlying observations.