Inference for covariate adjusted regression via varying coefficient models

By Damla cSenturk, H. Muller. 2006

84 citations recorded by the source corpus.

We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable covariate, where one specific distorting function is associated with each predictor or response. The dependence of both response and predictors on the same confounding covariate may alter the underlying regression relation between undistorted but unobserved predictors and response. We consider a class of highly flexible adjustment methods for parameter estimation in the underlying regression model, which is the model of interest. Asymptotic normality of the estimates is obtained by establishing a connection to varying coefficient models. These distribution results combined with proposed consistent estimates of the asymptotic variance are used for the construction of asymptotic confidence intervals for the regression coefficients. The proposed approach is illustrated with data on serum creatinine, and finite sample properties of the proposed procedures are investigated through a simulation study.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0fe5c3a002732ff977dee44dd5ae9fa7701f6ebe

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In Statistics and Probability

1. H. Muller
2. Peter Hall
3. Aurore Delaigle
4. Damla Sentürk
5. Hua Liang
6. Jun Zhang
7. Yao Yu
8. Li-Xing Zhu

Citations in the corpus

• Covariate-adjusted nonlinear regression (2009, background): “The estimators were further proved to be asymptotically normal by Sentürk and Müller (2006).”
• Nonparametric covariate-adjusted regression (2016, methodology): “In (B3), we relax the conventional boundedness condition on the covariates used by Şentürk and Müller (2005a, 2006) and Mammen et al. (2012), and assume instead that X has a finite exponential moment (for example this is satisfied if the distribution of X comes from the exponential family or is…”
• Partial linear single index models with distortion measurement errors (2013, methodology): “The second statement of Condition (A7) is a common condition on φ(u) andψr (u)s in the covariate-adjusted models (Şentürk and Müller 2005; Şentürk and Müller 2006, 2009).”
• Covariate Adjusted Correlation Analysis via Varying Coefficient Models (2005, methodology): “Using this result, Lemma 4(a,b) and (22) of Şentürk & Müller (2005b), (25), property (b), law of large numbers and boundedness considerations, it holds that r̂n13 ¼ g1 1 n X j wðU 0 njÞ/ðU 0 njÞ X 0nj s2X 0nj X k X 0njkY 0 njke 0 YX ;njk X 0nj X k Y 0njke 0 YX ;njk ! þ c1 1 n X j wðU 0 njÞ/ðU 0…”