Research Article Open Access

Quantile Regression Estimation Using Non-Crossing Constraints

Ilaria Lucrezia Amerise1
  • 1 Università della Calabria, Italy

Abstract

In this article we are concerned with a collection of multiple linear regressions that enable the researcher to gain an impression of the entire conditional distribution of a response variable given a set of explanatory variables. More specifically, we investigate the advantage of using a new method to estimate a bunch of non-crossing quantile regressions hyperplanes. The main tool is a weighting system of the data elements that aims to reduce the effect of contamination of the sampled population on the estimated parameters by diminishing the effect of outliers. The performances of the new estimators are evaluated on a number of data sets. We had considerable success with avoiding intersections and in the same time improving the global fitting of conditional quantile regressions. We conjecture that in other situations (e.g., data with high level of skewness, non-constant variances, unusual and imputed data) the method of weighted non-crossing quantiles will lead to estimators with good robustness properties.

Journal of Mathematics and Statistics
Volume 14 No. 1, 2018, 107-118

DOI: https://doi.org/10.3844/jmssp.2018.107.118

Submitted On: 15 February 2018 Published On: 15 May 2018

How to Cite: Amerise, I. L. (2018). Quantile Regression Estimation Using Non-Crossing Constraints. Journal of Mathematics and Statistics, 14(1), 107-118. https://doi.org/10.3844/jmssp.2018.107.118

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Keywords

  • Conditional Quantiles
  • Monotonicity Problem
  • Estimation Under Constraints