论文标题
非参数模型的可再生复合分位数方法和算法与流数据
Renewable Composite Quantile Method and Algorithm for Nonparametric Models with Streaming Data
论文作者
论文摘要
我们对具有流数据的非参数模型的可再生估计和算法感兴趣。在我们的方法中，非参数功能通过功能取决于重量函数和条件分布函数（CDF）表达。 CDF通过可再生内核估计与功能插值相结合，基于我们提出可再生加权复合分位数回归（WCQR）的方法。然后，我们完全使用模型结构并为重量函数获得新的选择器，以便在估计模型中的特定函数时，WCQR可以实现渐近无偏见。我们还提出了用于流数据的实用带宽选择器，并找到最佳的重量函数最小化渐近方差。渐近结果表明，我们的估计器几乎等同于从整个数据中获得的甲骨文估计器。此外，我们的方法还可以适应错误分布，对异常值的鲁棒性以及估计和计算的效率。模拟研究和实际数据分析进一步证实了我们的理论发现。
We are interested in renewable estimations and algorithms for nonparametric models with streaming data. In our method, the nonparametric function of interest is expressed through a functional depending on a weight function and a conditional distribution function (CDF). The CDF is estimated by renewable kernel estimations combined with function interpolations, based on which we propose the method of renewable weighted composite quantile regression (WCQR). Then we fully use the model structure and obtain new selectors for the weight function, such that the WCQR can achieve asymptotic unbiasness when estimating specific functions in the model. We also propose practical bandwidth selectors for streaming data and find the optimal weight function minimizing the asymptotic variance. The asymptotical results show that our estimator is almost equivalent to the oracle estimator obtained from the entire data together. Besides, our method also enjoys adaptiveness to error distributions, robustness to outliers, and efficiency in both estimation and computation. Simulation studies and real data analyses further confirm our theoretical findings.
