New designs to consistently estimate the isotonic regression

The usual estimators of the regression under isotonicity assumptions are too sensitive at the tails. In order to avoid this problem, some new strategies for fixed designs are analyzed. The uniform consistency of certain estimators on a closed and bounded working interval are obtained. It is shown th...

Full description

Saved in:
Bibliographic Details
Published in:Computational statistics 2018-06, Vol.33 (2), p.639-658
Main Authors: Colubi, Ana, Dominguez-Menchero, J. Santos, Gonzalez-Rodriguez, Gil
Format: Article
Language:English
Subjects:
Band theory
Economic Theory/Quantitative Economics/Mathematical Methods
Estimators
Interval arithmetic
Isotonicity
Mathematics and Statistics
Original Paper
Probability and Statistics in Computer Science
Probability Theory and Stochastic Processes
Regression analysis
Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The usual estimators of the regression under isotonicity assumptions are too sensitive at the tails. In order to avoid this problem, some new strategies for fixed designs are analyzed. The uniform consistency of certain estimators on a closed and bounded working interval are obtained. It is shown that the usual isotonic regression can be employed when the number of observations at the edges of the interval is suitably controlled. Moreover, two modifications are proposed which substantially improve the results. One modification is based on the reallocation of part of the edge observations, and the other one forces the isotonic regression to take values within some horizontal bands. The theoretical results are complemented with some examples and simulation studies that illustrate the performance of the proposed estimators in practice.
ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-018-0792-0