Composite Estimation for Single‐Index Models with Responses Subject to Detection Limits
针对因检测限导致左删失的响应变量，提出一种半参数估计方法，通过结合多个分位数水平的信息来估计单指标模型的连接函数和指标参数，避免参数分布假设，并在模拟和HIV抗体数据中验证了有效性。
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.