论文信息 - Covariate Adjusted Correlation Analysis via Varying Coefficient Models

Covariate Adjusted Correlation Analysis via Varying Coefficient Models

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. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..

Damla Şentürk | Hans-Georg Müller | H. Müller | D. Şentürk

[1] D. Rubinfeld,et al. Hedonic housing prices and the demand for clean air , 1978 .

[2] Xin-Yuan Song,et al. Local Polynomial Fitting in Semivarying Coefficient Model , 2002 .

[3] Damla Şentürk,et al. Inference for covariate adjusted regression via varying coefficient models , 2006 .

[4] Li Ping Yang,et al. Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data , 1998 .

[5] Chin-Tsang Chiang,et al. Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables , 2001 .

[6] D. McLeish. Dependent Central Limit Theorems and Invariance Principles , 1974 .

[7] R. Tibshirani,et al. Varying‐Coefficient Models , 1993 .

[8] Karl Pearson,et al. Karl Pearson's early statistical papers , 1948 .

[9] Damla Şentürk,et al. Covariate-adjusted regression , 2005 .

[10] Chin-Tsang Chiang,et al. KERNEL SMOOTHING ON VARYING COEFFICIENT MODELS WITH LONGITUDINAL DEPENDENT VARIABLE , 2000 .

[11] Jianqing Fan,et al. Efficient Estimation and Inferences for Varying-Coefficient Models , 2000 .

[12] H. Robbins,et al. Strong consistency of least squares estimates in multiple regression. , 1979, Proceedings of the National Academy of Sciences of the United States of America.