Advances and Applications in Statistics
Volume 49, Issue 6, Pages 417 - 441
(December 2016) http://dx.doi.org/10.17654/AS049060417 |
|
ITERATIVELY REWEIGHTED CONSTRAINED QUANTILE REGRESSIONS
Ilaria L. Amerise
|
Abstract: In this study, we propose a new estimation method for the parameters of a system of quantile regressions which overcomes the quantile-crossing problem. The main tools employed are: (1) a reformulation of the quantile regression problem in terms of linear programming which incorporates the non-crossing constraints in a sequential form and (2) the use of iteratively adjusted weights that are attached to the design points.
The performance of the proposed estimator is evaluated on a number of data sets and compared with other methods. For this purpose, we introduce a testing methodology that takes into account the global goodness-of-fit of multiple quantile regressions. We had considerable success in avoiding intersections and, at the same time, improving the fit to the data. Thus, we conjecture that, in the presence of bad measurements (e.g. data with high skewness, deviant observations and uncertain data), the new strategy of quantile regression will lead to estimators with good robustness properties. |
Keywords and phrases: linear programming, monotonicity, performance evaluation, global goodness-of-fit. |
|
Number of Downloads: 427 | Number of Views: 1313 |
|