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We propose a new estimation method to estimate the nonparametric functions in additive models, where the response is subject to fixed censoring. Under some regularity conditions, we show that the proposed estimator is uniformly consistent with certain convergence rates. The simulation study shows that the proposed estimator performs well in finite sample sizes. We also analyze a dataset from an HIV study for an illustration. [ABSTRACT FROM AUTHOR]

Abstract: We propose a semiparametric estimator for single‐index models with censored responses due to detection limits. In the presence of left censoring, the mean function cannot be identified without any parametric distributional assumptions, but the quantile function is still identifiable at upper quantile levels. To avoid parametric distributional assumption, we propose to fit censored quantile regression and combine information across quantile levels to estimate the unknown smooth link function and the index parameter. Under some regularity conditions, we show that the estimated link function achieves the non‐parametric optimal convergence rate, and the estimated index parameter is asymptotically normal. The simulation study shows that the proposed estimator is competitive with the omniscient least squares estimator based on the latent uncensored responses for data with normal errors but much more efficient for heavy‐tailed data under light and moderate censoring. The practical value of the proposed method is demonstrated through the analysis of a human immunodeficiency virus antibody data set. [ABSTRACT FROM AUTHOR]

In this paper, we consider two weighted estimators to improve estimation efficiency in quantile regression with longitudinal data. The first estimator is from weighted quantile regression, and the second estimator is from weighted composite quantile regression, where the weights in the second estimator are from the first estimator. Different from earlier literature, our weights are quantile adaptive, which borrow information from the intra-subject correlation of the conditional quantile scores, rather than the conditional least squares scores. The weight for each subject is obtained from smoothed empirical likelihood quantile estimator, where quadratic inference function method is used to model the inverse of the correlation matrix of the conditional quantile scores. Under some regularity conditions, we prove that the weighted estimators are more efficient than the standard quantile regression estimators with equal weights. We conduct a simulation study and a real data analysis to evaluate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]