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Covariate Adjusted Correlation Analysis via Varying Coefficient Models

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  • DAMLA ŞENTÜRK
  • HANS‐GEORG MÜLLER

Abstract

. We propose covariate adjusted correlation (Cadcor) analysis to target the correlation between two hidden variables that are observed after being multiplied by an unknown function of a common observable confounding variable. The distorting effects of this confounding may alter the correlation relation between the hidden variables. Covariate adjusted correlation analysis enables consistent estimation of this correlation, by targeting the definition of correlation through the slopes of the regressions of the hidden variables on each other and by establishing a connection to varying‐coefficient regression. The asymptotic distribution of the resulting adjusted correlation estimate is established. These distribution results, when combined with proposed consistent estimates of the asymptotic variance, lead to the construction of approximate confidence intervals and inference for adjusted correlations. We illustrate our approach through an application to the Boston house price data. Finite sample properties of the proposed procedures are investigated through a simulation study.

Suggested Citation

  • Damla Şentürk & Hans‐Georg Müller, 2005. "Covariate Adjusted Correlation Analysis via Varying Coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 365-383, September.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:3:p:365-383
    DOI: 10.1111/j.1467-9469.2005.00450.x
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    Cited by:

    1. Zhang, Jun & Zhu, Li-Ping & Zhu, Li-Xing, 2012. "On a dimension reduction regression with covariate adjustment," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 39-55, February.
    2. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
    3. Zongwu Cai, 2013. "Functional Coefficient Models for Economic and Financial Data," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.

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