A robust test of specification based on order statistics

The test of misspecification presented compares parametric and nonparametric regressions. The latter is estimated using order statistics, which provide robust and distribution free estimators. The former is estimated using, in turn, least squares and least absolute deviation (LAD). When implementing LAD, robust and distribution free estimators are considered in both parametric and nonparametric regressions. This defines a very homogeneous test which can discriminate misspecification from the impact of outliers and/or skewness. These two effects are instead mixed together in the tests comparing OLS with nonparametric estimators, potentially driving to erroneous conclusions. An example and a Monte Carlo experiment analyze the behavior of the proposed test.