In the past two decades,model averaging,as a way to solve model uncertainty,has attracted more and more attention.In this paper,the authors propose a jackknife model averaging(JMA) method for the quantile single-index coefficient model,which is widely used in statistics.Under model misspecification,the model averaging estimator is proved to be asymptotically optimal in terms of minimizing out-of-sample quantile loss.Simulation experiments are conducted to compare the JMA method with several model selections and model averaging methods,and the results show that the proposed method has a satisfactory performance.The method is also applied to a real dataset.
The battery thermal management of electric vehicles can be improved using neural networks predicting quantile sequences of the battery temperature.This work extends a method for the development of Quantile Convolutional and Quantile Recurrent Neural Networks(namely Q*NN).Fleet data of 225629 drives are clustered and balanced,simulation data from 971 simulations are augmented before they are combined for training and testing.The Q*NN hyperparameters are optimized using an efficient Bayesian optimization,before the Q*NN models are compared with regression and quantile regression models for four horizons.The analysis of point-forecast and quantile-related metrics shows the superior performance of the novel Q*NN models.The median predictions of the best performing model achieve an average RMSE of 0.66°C and R^(2) of 0.84.The predicted 0.99 quantile covers 98.87%of the true values in the test data.In conclusion,this work proposes an extended development and comparison of Q*NN models for accurate battery temperature prediction.
Andreas M.BillertRunyao YuStefan ErschenMichael FreyFrank Gauterin
In this paper,the authors propose a two-stage online debiased lasso estimation and statistical inference method for high-dimensional quantile regression(QR)models in the presence of streaming data.In the first stage,the authors modify the QR score function based on kernel smoothing and obtain the online lasso smoothed QR estimator through iterative algorithms.The estimation process only involves the current data batch and specific historical summary statistics,which perfectly accommodates to the special structure of streaming data.In the second stage,an online debiasing procedure is carried out to eliminate biases caused by the lasso penalty as well as the accumulative approximation error so that the asymptotic normality of the resulting estimator can be established.The authors conduct extensive numerical experiments to evaluate the performance of the proposed method.These experiments demonstrate the effectiveness of the proposed method and support the theoretical results.An application to the Beijing PM2.5 Dataset is also presented.
In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters.Different from the traditional model averaging for quantile regression which considers only a single quantile,the proposed model averaging estimator is based on multiple quantiles.The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights.The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error.Simulation studies are conducted to demonstrate the finite sample performance of the new model averaging estimator.The proposed method is also applied to the analysis of the stock returns data and the wage data.
