Non parametric maximin aggregation for data with inhomogeneity

Data are heterogeneous when recorded in different time regimes or taken from multiple sources to some degree. Varying-coefficient models or mixture models are suitable for solving this type of problem. On one hand, existing models are quite complicated and computationally cumbersome especially for large-scale data. On the other hand, common effects among different data sources are unknown. Additionally, some existing models are unable to search the non linear relationship between response and covariates. To address these challenges, we aim at estimating common effects about non parametric regression when data are heterogeneous. Our proposed estimation method is based on basis function expansion. Adaptive basis series and fixed basis series are considered, respectively. We exploit maximin aggregation technique to get a simple non linear model, also the common effects, from all possible grouped data. The mean squared error and asymptotic distribution of the estimator are investigated. Simulation studies and real-data analysis are conducted to verify the efficiency of the estimation procedure. Comparing with ordinary least square estimator and averaging ordinary least square estimator, our proposed estimator can reduce the complexity of data sources and is more robust.