The asymptotic distribution of the isotonic regression estimator over a general countable pre-ordered set

Research output: Contribution to journalArticle

Abstract

We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution of the isotonized estimator is given by the concatenation of the separate isotonic regressions of the certain subvectors of an unrestrecred estimator’s asymptotic distribution. Also, we show that the isotonization preserves the rate of convergence of the underlying estimator. We apply these results to the problems of estimation of a bimonotone regression function and estimation of a bimonotone probability mass function.

Details

Authors
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Probability Theory and Statistics

Keywords

  • Constrained inference, Isotonic regression, Limit distribution
Original languageEnglish
Pages (from-to)4180-4208
Number of pages29
JournalElectronic Journal of Statistics
Volume12
Issue number2
Publication statusPublished - 2018
Publication categoryResearch
Peer-reviewedYes