Model averaging marginal regression for high dimensional conditional quantile prediction
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Model averaging marginal regression for high dimensional conditional quantile prediction Jingwen Tu1 · Hu Yang1 · Chaohui Guo1,2 · Jing Lv3 Received: 3 April 2020 / Revised: 26 September 2020 / Accepted: 11 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this article, we propose a high dimensional semiparametric model average approach to predict the conditional quantile of the response variable. Firstly, we approximate the multivariate conditional quantile function by an affine combination of one-dimensional marginal conditional quantile functions which can be estimated by the local linear regression. Secondly, based on the estimated marginal quantile regression functions, a penalized quantile regression is proposed to estimate and select the significant model weights involved in the approximation. Under some mild conditions, we have established the asymptotic properties for both the parametric and nonparametric estimators. Finally, we evaluate the finite sample performance of the proposed procedure via simulations and a real data analysis. Keywords Kernel estimation · Marginal regression · Model averaging · Penalized quantile regression · Prediction accuracy
1 Introduction In many practical situations, especially for economic and medical fields, forecasting and predictive inference are our main goals. Model averaging method is useful for prediction by fitting a large number of candidate models and giving higher weights to the better candidate models. Therefore, model averaging technique substantially reduces the risk of misspecification and improves the prediction accuracy. Earlier results on
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00362020-01212-1) contains supplementary material, which is available to authorized users.
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Chaohui Guo [email protected]
1
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
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College of Mathematics Science, Chongqing Normal University, Chongqing 401331, China
3
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
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J. Tu et al.
Bayesian model averaging include Hoeting et al. (1999), Raftery et al. (1997) and Hjort and Claeskens (2003). Recently, various strategies have been developed for frequentist model averaging. For example, Hansen (2007) selected the model weights by minimizing a Mallows criterion and showed that their proposed estimator is asymptotically optimal in the sense of achieving the lowest possible squared error under a class of discrete model average estimators. Wan et al. (2010) focused on two assumptions of Hansen (2007) and provided a stronger theoretical basis for the use of the Mallows criterion in model averaging. To deal with heteroscedastic data, Hansen and Racine (2012) developed a jackknife model averaging approach to select the model weights by minimizing a cross-validation criterion and proved that their proposed approach is asymptotically optimal in the sense of achieving the lo
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