Locally penalized single-index model using B-splines and spherical coordinates

In this study, we focus on the estimation of regression function in single-index model based B-splines using penalization techniques. We adopt a spherical coordinates reparameterization an index vector to deal with identification problem model. To provide spatially adaptive method, two types penalties are applied and function. A special penalty called localized is introduced handle sparsity coordinates, total variation considered smoothing Using coordinate descent algorithm grid search tuning parameters, entire solution paths coefficients functions for parameters can be obtained efficiently. The performance proposed estimator studied through both numerical simulations real data sets. An R software package pbssim available.