This paper studies various aspects of shrinkage and selection procedures based on L-estimation, one of the important methods of robust estimation. We know that median is better than mean whenever outliers are present in the sample. In this paper, we increase the number of quantiles to improve the efficiency to nearly full sample efficiency. In addition, we study the comparative properties of the unrestricted, restricted, preliminary test, Saleh-type estimator, LASSO and ridge-type estimator, and elastic net penalty-based estimator of the location parameter of a continuous distribution function, \(F_{0}(\frac {y - \theta }{\sigma })\) , and the density function, \(\frac {1}{\sigma } f_{0}\left (\frac {y - \theta }{\sigma }\right )\) , based on a subset of order statistics from a sample of size \(n (\ge 1).\) Optimum spacing and coefficients of linearity are provided for the logistic distribution as an example. We use the usual consistent estimators for the unknown c.d.f. and p.d.f. for the coefficients of L-estimation.