Partially Linear Models with Missing Response Variables and Error-prone Covariates. Academic Article

abstract

• We consider partially linear models of the form Y = X(T)beta + nu(Z) + epsilon when the response variable Y is sometimes missing with missingness probability pi depending on (X, Z), and the covariate X is measured with error, where nu(z) is an unspecified smooth function. The missingness structure is therefore missing not at random, rather than the usual missing at random. We propose a class of semiparametric estimators for the parameter of interest beta, as well as for the population mean E(Y). The resulting estimators are shown to be consistent and asymptotically normal under general assumptions. To construct a confidence region for beta, we also propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. The proposed methods are applied to an AIDS clinical trial dataset. A simulation study is also reported.

authors

• Carroll, Raymond

published proceedings

• Biometrika

author list (cited authors)

• Liang, H., Wang, S., & Carroll, R. J.

citation count

• 99

complete list of authors

• Liang, Hua||Wang, Suojin||Carroll, Raymond J

publication date

• March 2007

publisher

• Oxford University Press (OUP)  Publisher

published in

• Biometrika  Journal

keywords

• Confidence Region
• Empirical Likelihood
• Estimating Equation
• Measurement Error
• Missing Data
• Missing Not At Random
• Nonparametric Regression
• Semiparametric Estimation

PubMed Central ID

• 20209027

Digital Object Identifier (DOI)

• 10.1093/biomet/asm010

start page

• 185

end page

• 198

volume

• 94

issue

• 1

URL

• http%3A%2F%2Fdx.doi.org%2F10.1093%2Fbiomet%2Fasm010