Two common problems in applied statistics are multicollinearity between variables and the presence of outliers in the data. In a partially linear regression model, a family of robust ridge estimators for the regression parameters and the nonlinear part is introduced by adding an $L_2$ penalty to the well-known least trimmed squares estimator. The partial residual estimation method with the Gasser–Müller estimator is applied for the estimation of the nonlinear part. The breakdown point of these estimators are derived and the FAST-LTS algorithm is described for the computation of the estimators. Furthermore, a method for the simultaneous choice of the ridge and bandwidth parameters is developed. The proposed method is applied to the housing prices data set and a Monté-Carlo simulation study is conducted to examine the efficiency of the estimators.

This article is concerned with nonparametric estimation of the entropy in ranked set sampling. Theoretical properties of the proposed estimator are studied. The proposed estimator is compared with the rival estimator in simple random sampling. The applications of the proposed estimator to the mutual information estimation as well as estimation of the Kullback–Leibler divergence are provided. Several Monté-Carlo simulation studies are conducted to examine the performance of the estimator. The results are applied to the longleaf pine (Pinus palustris) trees and the body fat percentage datasets to illustrate applicability of theoretical results.