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Influence Measures in Quantile Regression Models

In this article, we use the asymmetric Laplace distribution to define a new method to determine the influence of a certain observation in the fit of quantile regression models. Our measure is based on the likelihood displacement function and we propose two types of measures in order to determine influential observations in a set of conditional quantiles conjointly or in each conditional quantile of interest. We verify the validity of our average measure in a simulated data set as well in an illustrative example with data about air pollution.