zbMATH — the first resource for mathematics

Asymptotic properties of covariate-adjusted regression with correlated errors. (English) Zbl 1160.62079
Summary: In covariate-adjusted regression (CAR), the response \((Y)\) and the predictors \((X_r,r=1,\dots ,p)\) are not observed directly. The estimation is based on \(n\) independent observations \(\{\tilde Y_i,\tilde X_{ri}, U_i\}_{i=1}^n\), where \(\tilde Y_i = \psi (U_i)Y_i,\tilde X_{ri} = \phi _r (U_i)X_{ri}\) and \(\psi (\cdot)\) and \(\{\phi _r(\cdot )\}^p_{r=1}\) are unknown functions. We discuss the asymptotic properties of this method when the observations are correlated, as in regression models for repeated measurements.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
62M20 Inference from stochastic processes and prediction
Full Text: DOI
[1] Hastie, T.; Tibshirani, R., Varying coefficient models, J. R. stat. soc. B., 55, 757-796, (1993) · Zbl 0796.62060
[2] Kaysen, G.A.; Dubin, J.A.; Müller, H.G.; Mitch, W.E.; Rosales, L.M.; Levin, N.W., Relationship among inflammation nutrition and physiologic mechanisms establishing albumin levels in hemodialysis patients, Kidney int., 61, 2240-2249, (2002)
[3] Nguyen, D.V., Şentürk, D., 2009. Covariate-adjusted regression for longitudinal data incorporating correlation between repeated measurements. Austral. N. Z. J. Stat. (in press)
[4] Şentürk, D.; Müller, H.G., Covariate-adjusted regression, Biometrika, 92, 75-89, (2005) · Zbl 1068.62082
[5] Şentürk, D.; Müller, H.G., Inference for covariate-adjusted regression via varying coefficient models, Ann. statist., 34, 654-679, (2006) · Zbl 1095.62045
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.