Title: Grid Point Approximation for Distributed Nonparametric Smoothing and Prediction Show Chinese title

Title: 分布式非参数平滑和预测的网格点逼近

Abstract: Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we find that the popularly used one-shot type estimator is highly inefficient for prediction purposes. To this end, we propose a novel grid point approximation (GPA) method, which has the following advantages. First, the resulting GPA estimator is as statistically efficient as the global estimator under mild conditions. Second, it requires no communication and is extremely efficient in terms of computation for prediction. Third, it is applicable to the case where the data are not randomly distributed across different machines. To select a suitable bandwidth, two novel bandwidth selectors are further developed and theoretically supported. Extensive numerical studies are conducted to corroborate our theoretical findings. Two real data examples are also provided to demonstrate the usefulness of our GPA method. Show Chinese abstract

Abstract: 核平滑是现代统计分析中广泛使用的一种非参数方法。 在分布式系统上对大规模数据集进行高效核平滑的问题是一个非常重要问题。 在本工作中，我们发现广泛使用的单次类型估计量在预测方面效率非常低。 为此，我们提出了一种新颖的网格点近似（GPA）方法，具有以下优点。 首先，在适度条件下，所得的GPA估计量在统计效率上与全局估计量相当。 其次，它不需要通信，在计算方面对于预测来说极其高效。 第三，它适用于数据在不同机器上不是随机分布的情况。 为了选择合适的带宽，进一步开发了两种新的带宽选择器，并有理论支持。 进行了广泛的数值研究以验证我们的理论结果。 还提供了两个实际数据例子来展示我们GPA方法的实用性。