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

Jingwei Wu1, Hanxiang Peng2, Wanzhu Tu3

  • 1Department of Epidemiology and Biostatistics, College of Public Health, Temple University, Philadelphia, PA 19122.

Journal of Multivariate Analysis
|October 8, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a multivariate single-index model (SIM) for creating medical indices with multiple outcomes. The research establishes theoretical properties for SIM parameter estimators, enabling formal statistical inference for complex medical index development.

Keywords:
Asymptotic normalityConsistencyMixed effect modelMultivariate outcomesP-splinesSingle-index models

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Area of Science:

  • Biostatistics
  • Medical Informatics
  • Epidemiology

Background:

  • Developing medical indices often involves multiple health outcomes.
  • Existing single-index models (SIMs) primarily focus on univariate outcomes.
  • Theoretical properties of multivariate SIM parameter estimators remain understudied, limiting formal inference.

Purpose of the Study:

  • To propose and analyze a multivariate single-index model (SIM) for medical index development.
  • To investigate the asymptotic properties of parameter estimators in multivariate SIMs.
  • To provide a formal inference procedure for multivariate SIMs.

Main Methods:

  • Optimization of index functions against diverse outcomes.
  • Representation of multivariate SIMs as sums of univariate SIMs.
  • Examination of asymptotic properties (n-consistency and asymptotic normality) of parameter estimators.
  • Simulation studies for finite-sample performance evaluation.

Main Results:

  • Multivariate SIM parameter estimators are shown to be n-consistent and asymptotically normal under mild regularity conditions.
  • A simulation study confirmed the performance of estimation and inference procedures.
  • The study demonstrates the practical application of the multivariate SIM.

Conclusions:

  • The proposed multivariate SIM offers a robust framework for developing medical indices with multiple outcomes.
  • The established asymptotic properties provide a foundation for formal statistical inference in multivariate SIMs.
  • The model is applicable in real-world scenarios, such as assessing hypertension risk using urine electrolyte markers.