Analysis of Double Single Index Models

Kun Chen, Yanyuan Ma

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Motivated from problems in canonical correlation analysis, reduced rank regression and sufficient dimension reduction, we introduce a double dimension reduction model where a single index of the multivariate response is linked to the multivariate covariate through a single index of these covariates, hence the name double single index model. Because nonlinear association between two sets of multivariate variables can be arbitrarily complex and even intractable in general, we aim at seeking a principal one-dimensional association structure where a response index is fully characterized by a single predictor index. The functional relation between the two single-indices is left unspecified, allowing flexible exploration of any potential nonlinear association. We argue that such double single index association is meaningful and easy to interpret, and the rest of the multi-dimensional dependence structure can be treated as nuisance in model estimation. We investigate the estimation and inference of both indices and the regression function, and derive the asymptotic properties of our procedure. We illustrate the numerical performance in finite samples and demonstrate the usefulness of the modelling and estimation procedure in a multi-covariate multi-response problem concerning concrete.

Original languageEnglish (US)
Pages (from-to)1-20
Number of pages20
JournalScandinavian Journal of Statistics
Volume44
Issue number1
DOIs
StatePublished - Mar 1 2017

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Single-index Model
Covariates
Reduced Rank Regression
Sufficient Dimension Reduction
Multivariate Response
Canonical Correlation Analysis
Dependence Structure
Dimension Reduction
Regression Function
Index model
Asymptotic Properties
Predictors
Modeling
Model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Analysis of Double Single Index Models. / Chen, Kun; Ma, Yanyuan.

In: Scandinavian Journal of Statistics, Vol. 44, No. 1, 01.03.2017, p. 1-20.

Research output: Contribution to journalArticle

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