Score estimation of monotone partially linear index model

Mengshan Xu, Taisuke Otsu

Research output: Contribution to journalArticlepeer-review


This paper studies semiparametric estimation of a partially linear single index model with a monotone link function. Our estimator is an extension of the score-type estimator developed by Balabdaoui et al. (2019) for the monotone single index model, which profiles out the unknown link function by isotonic regression. An attractive feature of the proposed estimator is that it is free from tuning parameters for nonparametric smoothing. We show that our estimator for the finite-dimensional components is (Formula presented.) -consistent and asymptotically normal. By introducing an additional smoothing to obtain the efficient score, we propose an asymptotically efficient estimator for the finite-dimensional components. Furthermore, we establish the asymptotic validity of a bootstrap inference method based the score-type estimator, which is also free from tuning parameters. A simulation study illustrates the usefulness of the proposed method.

Original languageEnglish
Pages (from-to)838-863
Number of pages26
JournalJournal of Nonparametric Statistics
Issue number4
Publication statusPublished - 2020 Dec
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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