α-Optimal Subsampling for Joint Mean and Variance Models Under Heteroscedasticity Big Data
With the development of information technology,an unusually large amount of data is generated in economy,finance,industry and other fields,and these data have the characteristics of heteroscedasticity.The traditional statistical models and statistical methods can not solve the heteroscedasticity modeling problem in big data.Subsampling is an important method to deal with big data.In this paper,we study the subsampling for the joint mean and variance models in the heteroskedas-tic big data environment.The main contributions of this paper are as follows:The joint mean and variance models are developed for heteroscedasticity big data,and the consistency and asymptotic normality of the subsample estimator are proven based on the A-optimality criterion and the L-optimality criterion under certain conditions;An α-optimal subsampling algorithm of the joint mean and variance models for het-eroscedasticity big data is proposed.The results of numerical simulations and a real example show that the sampling algorithm improves estimation accuracy and reduces computational costs.
Heteroscedasticity big datajoint mean and variance modelsα-optimal subsampling
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