<p>Modal regression uses the conditional mode to explain the dependent variable and has good robustness when the dataset contains outliers or the error distribution is heavy-tailed or asymmetric. For the varying coefficient modal regression model, some scholars have proposed local modal estimation for coefficient functions using the local polynomial method. Since the same bandwidth is applied for each coefficient function, when the smoothness of coefficient functions is different, the efficiency of the local estimation method will decrease. This paper proposes global estimation methods for the varying coefficient modal regression model, which allow different bandwidths to be used for each coefficient function, thus improving the estimation accuracy, especially when the smoothness of the coefficient functions is significantly different. The asymptotic properties of the proposed estimators are proved in this paper. The numerical simulation shows that the global methods perform better than the local method, and a real data analysis is also provided.</p>

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Efficient estimation for varying coefficient modal regression

  • Ruonan Cheng,
  • Xiuqing Zhou

摘要

Modal regression uses the conditional mode to explain the dependent variable and has good robustness when the dataset contains outliers or the error distribution is heavy-tailed or asymmetric. For the varying coefficient modal regression model, some scholars have proposed local modal estimation for coefficient functions using the local polynomial method. Since the same bandwidth is applied for each coefficient function, when the smoothness of coefficient functions is different, the efficiency of the local estimation method will decrease. This paper proposes global estimation methods for the varying coefficient modal regression model, which allow different bandwidths to be used for each coefficient function, thus improving the estimation accuracy, especially when the smoothness of the coefficient functions is significantly different. The asymptotic properties of the proposed estimators are proved in this paper. The numerical simulation shows that the global methods perform better than the local method, and a real data analysis is also provided.