Adaptively aggregated forecast for exponential family panel model

Aggregation strategies play an important role akin to that of model selection and have been extensively studied in different statistical models to improve forecasting accuracy. However, traditional aggregated forecast strategies for panel data are mainly developed under the assumption that response variables are continuously distributed (or normally distributed). Replacing this assumption by a more general family of distributions, i.e., exponential family distributions, this paper proposes a computationally efficient way to construct the cumulative risk function and to explicitly accommodate the correlation structure of within-subject observations, develops two novel adaptively aggregated forecasting strategies via exponential reweighting and quadratic reweighting, and rigorously establishes the corresponding tight oracle inequalities. The proposed exponential reweighting-based strategy enjoys promising Kullback–Leibler risk-bound adaptation. Moreover, under the quadratic risk, a promising adaptation property can be achieved by the quadratic reweighting-based strategy. The risk-bound properties of the two proposed procedures in the presence of pre-screening are established under mild conditions. The calibration properties of the proposed methods are also analyzed. Simulation studies, together with an example in analyzing television viewers’ binary decision sequence of watching drama episodes, verify the superiority of our methods over existing model selection and aggregation methods.