  In this paper, the problem of robust estimation and validation of
location-scale families is revisited. The proposed methods exploit the joint
asymptotic normality of sample quantiles (of i.i.d random variables) to
construct the ordinary and generalized least squares estimators of location and
scale parameters. These quantile least squares (QLS) estimators are easy to
compute because they have explicit expressions, their robustness is achieved by
excluding extreme quantiles from the least-squares estimation, and efficiency
is boosted by using as many non-extreme quantiles as practically relevant. The
influence functions of the QLS estimators are specified and plotted for several
location-scale families. They closely resemble the shapes of some well-known
influence functions yet those shapes emerge automatically (i.e., do not need to
be specified). The joint asymptotic normality of the proposed estimators is
established, and their finite-sample properties are explored using simulations.
Also, computational costs of these estimators, as well as those of MLE, are
evaluated for sample sizes n = 10^6, 10^7, 10^8, 10^9. For model validation,
two goodness-of-fit tests are constructed and their performance is studied
using simulations and real data. In particular, for the daily stock returns of
Google over the last four years, both tests strongly support the logistic
distribution assumption and reject other bell-shaped competitors.
