Taipei: Institute of Statistical Science, Academia Sinica
For partial spline models with a monotone nonlinear component, a class of monotone estimating equations is proposed for estimating the slope parameters of the vector of covariables Z of the linear component, while adjusting for the corresponding ranks of the vector of covariables X of the nonlinear component. This approach avoids the technical complications due to the smoothing of estimators for the nonlinear component with monotonicity, as well as the curse of dimensionality. Also, computationally, our inferences do not involve the unknown error probability density function. As an R-estimator taking into account the rank correlation between Y and X, the asymptotic relative efficiency with respect to other estimators ignoring X is proportional to the Spearman correlation coefficient between them.