Sensivity functions and numerical analysis of the repeated median slope (Q1965974)

The authors consider the simple linear regression model \(y_i=\alpha+\beta x_i +\varepsilon_i\), \(i=1,\dots, n,\) where \(z_i=(x_i,y_i)\) are the observations and \(\varepsilon_i\) represent noise. It is assumed that \(x_i\) and \(\varepsilon_i\) are mutually independent with distributions \(G\) and \(F\), respectively. The repeated median slope estimate of the parameter \(\beta\) is investigated. The asymptotic behaviour of the estimate is investigated with the help of numerical analysis methods. Some graphical displays are provided to facilitate the interpretation.