Large-sample estimation and inference in multivariate single-index models

Jingwei Wu, Hanxiang Peng, Wanzhu Tu

Research output: Contribution to journalArticle


By optimizing index functions against different outcomes, we propose a multivariate single-index model (SIM) for development of medical indices that simultaneously work with multiple outcomes. Fitting of a multivariate SIM is not fundamentally different from fitting a univariate SIM, as the former can be written as a sum of multiple univariate SIMs with appropriate indicator functions. What have not been carefully studied are the theoretical properties of the parameter estimators. Because of the lack of asymptotic results, no formal inference procedure has been made available for multivariate SIMs. In this paper, we examine the asymptotic properties of the multivariate SIM parameter estimators. We show that, under mild regularity conditions, estimators for the multivariate SIM parameters are indeed n-consistent and asymptotically normal. We conduct a simulation study to investigate the finite-sample performance of the corresponding estimation and inference procedures. To illustrate its use in practice, we construct an index measure of urine electrolyte markers for assessing the risk of hypertension in individual subjects.

Original languageEnglish (US)
Pages (from-to)382-396
Number of pages15
JournalJournal of Multivariate Analysis
StatePublished - May 2019


  • Asymptotic normality
  • Consistency
  • Mixed effect model
  • Multivariate outcomes
  • P-splines
  • Single-index models

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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