Mode Regression Of Streaming Data

With the rapid development of big data technology and the continuous expansion of its application scenarios,the processing of streaming data has become an important research topic.Stream datasets arrive continuously in a fast and unbounded manifold,with real-time and constantly changing characteristics.Therefore,special algorithms and models need to be used for processing and estimation,such as online update methods.This method integrates new data into existing data through incremental updates during the operation of the data processing system,thereby achieving dynamic updates and incremental calculations of the data.As a supplement to mean regression and quantile regression,mode regression has good robustness.When the data distribution is heavy tailed,biased,or multi peaked,mode regression can better describe the center of conditional distribution.This article is based on the idea of online updates and applies the updatable estimation method to the modal linear regression model scenario,iteratively updating the estimation of unknown parameters using the aggregated statistical data of current batch data and historical batch data.In order to achieve the optimal convergence speed of the estimator,this paper proposes adjusting the bandwidth based on the data volume of the newly arrived batch data stream,and theoretically proves that the proposed estimation method has the same asymptotic distribution as the estimation method that directly uses all datasets.Finally,the theoretical results are verified by Monte Carlo numerical simulation and the real data of the 2011-2020 monthly U.S.current population survey,and the good properties of the proposed updatable mode regression estimation method are verified.