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Analysis of Double Single Index Models.

Kun Chen1, Yanyuan Ma2

  • 1Department of Statistics, University of Connecticut, 215 Glenbrook Road U-4120, Storrs, Connecticut 06269, U.S.A.

Scandinavian Journal of Statistics, Theory and Applications
|March 21, 2017
PubMed
Summary
This summary is machine-generated.

We introduce a double single index model for analyzing complex multivariate relationships. This method simplifies high-dimensional data by identifying a principal one-dimensional association structure between response and predictor indices.

Keywords:
Canonical correlation analysisReduced rank regresionSemiparametric efficiencySingle index modelsSufficient dimension reduction

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Area of Science:

  • Statistics
  • Multivariate Analysis
  • Dimensionality Reduction

Background:

  • Canonical correlation analysis, reduced rank regression, and sufficient dimension reduction face challenges with complex multivariate data.
  • Existing methods may struggle to capture intricate nonlinear associations between multiple response and predictor variables.

Purpose of the Study:

  • To introduce a novel double single index model for uncovering principal one-dimensional association structures.
  • To flexibly explore unspecified nonlinear relationships between multivariate responses and covariates.
  • To provide a framework for estimating and inferring these indices and the regression function.

Main Methods:

  • Development of a double dimension reduction model linking a single index of multivariate responses to a single index of multivariate covariates.
  • Focus on identifying a principal one-dimensional association structure, treating remaining dependencies as nuisance.
  • Derivation of asymptotic properties for the proposed estimation and inference procedures.

Main Results:

  • The proposed double single index model effectively captures the primary one-dimensional association between response and predictor indices.
  • The method allows for flexible modeling of unspecified nonlinear functional relations.
  • Asymptotic properties of the estimation and inference procedures are theoretically established.

Conclusions:

  • The double single index model offers a meaningful and interpretable approach to multivariate data analysis.
  • This methodology is effective in simplifying complex dependencies, facilitating easier interpretation.
  • The model's practical utility is demonstrated in a concrete multi-covariate, multi-response problem.