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1.  Partially Linear Models with Missing Response Variables and Error-prone Covariates 
Biometrika  2007;94(1):185-198.
We consider partially linear models of the form Y = XTβ + ν(Z) + ε when the response variable Y is sometimes missing with missingness probability π depending on (X, Z), and the covariate X is measured with error, where ν(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 β, 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 β, 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.
PMCID: PMC2832298  PMID: 20209027
Confidence region; Empirical likelihood; Estimating equation; Measurement error; Missing data; Missing not at random; Nonparametric regression; Semiparametric estimation
2.  Tuning parameter selectors for the smoothly clipped absolute deviation method 
Biometrika  2007;94(3):553-568.
The penalised least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method. It not only automatically and consistently selects the important variables, but also produces estimators which are as efficient as the oracle estimator. However, these attractive features depend on appropriately choosing the tuning parameter. We show that the commonly used the generalised crossvalidation cannot select the tuning parameter satisfactorily, with a nonignorable overfitting effect in the resulting model. In addition, we propose a bic tuning parameter selector, which is shown to be able to identify the true model consistently. Simulation studies are presented to support theoretical findings, and an empirical example is given to illustrate its use in the Female Labor Supply data.
PMCID: PMC2663963  PMID: 19343105
aic; bic; Generalised crossvalidation; Least absolute shrinkage and selection operator; Smoothly clipped absolute deviation

Results 1-2 (2)