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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:171

Article

Wu, Jingwei¹  Peng, Hanxiang²  Tu, Wanzhu³ 

[1] Temple Univ, Coll Publ Hlth, Dept Epidemiol & Biostat, Philadelphia, PA 19122 USA

[2] Indiana Univ Purdue Univ, Dept Math Stat, Indianapolis, IN 46202 USA

[3] Indiana Univ Sch Med, Dept Biostat, Indianapolis, IN 46202 USA

关键词: Asymptotic normality;    Consistency;    Mixed effect model;    Multivariate outcomes;    P-splines;    Single-index models;   

DOI  :  10.1016/j.jmva.2019.01.003

来源: Elsevier

【 摘 要 】

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 root 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free