Generalized penalized least squares and its statistical characteristics

The solution properties of semiparametric model are analyzed, especially that penalized least squares for semiparametric model will be invalid when the matrixB ^T PB is ill-posed or singular. According to the principle of ridge estimate for linear parametric model, generalized penalized least squares for semiparametric model are put forward, and some formulae and statistical properties of estimates are derived. Finally according to simulation examples some helpful conclusions are drawn.