Stable prediction in high-dimensional linear models |
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Authors: | Bingqing Lin Qihua Wang Jun Zhang Zhen Pang |
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Institution: | 1.Institute of Statistical Sciences, College of Mathematics and Statistics,Shenzhen University,Shenzhen,China;2.Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing,China;3.Department of Applied Mathematics,The Hong Kong Polytechnic University,Kowloon,Hong Kong |
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Abstract: | We propose a Random Splitting Model Averaging procedure, RSMA, to achieve stable predictions in high-dimensional linear models. The idea is to use split training data to construct and estimate candidate models and use test data to form a second-level data. The second-level data is used to estimate optimal weights for candidate models by quadratic optimization under non-negative constraints. This procedure has three appealing features: (1) RSMA avoids model overfitting, as a result, gives improved prediction accuracy. (2) By adaptively choosing optimal weights, we obtain more stable predictions via averaging over several candidate models. (3) Based on RSMA, a weighted importance index is proposed to rank the predictors to discriminate relevant predictors from irrelevant ones. Simulation studies and a real data analysis demonstrate that RSMA procedure has excellent predictive performance and the associated weighted importance index could well rank the predictors. |
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