TITLE:
Predictions in Quantile Regressions
AUTHORS:
Marilena Furno
KEYWORDS:
Predictions, Quantile Regressions, Gradient
JOURNAL NAME:
Open Journal of Statistics,
Vol.4 No.7,
August
28,
2014
ABSTRACT: Two different tools to evaluate quantile regression
forecasts are proposed: MAD, to summarize forecast errors, and a fluctuation
test to evaluate in-sample predictions. The scores of the PISA test to evaluate
students’ proficiency are considered. Growth analysis relates school attainment
to economic growth. The analysis is complemented by investigating the estimated
regression and predictions not only at the centre but also in the tails. For
out-of-sample forecasts, the estimates in one wave are employed to forecast the
following waves. The reliability of in-sample forecasts is controlled by
excluding the part of the sample selected by a specific rule: boys to predict
girls, public schools to forecast private ones, vocational schools to predict
non-vocational, etc. The gradient computed in the subset is compared to its
analogue computed in the full sample in order to verify the validity of the
estimated equation and thus of the in-sample predictions.