Aggregated Expectile Regression by Exponential Weighting

Gu, Yuwen; Zou, Hui

doi:10.5705/ss.202016.0285

Cited by 3 publications

(9 citation statements)

References 34 publications

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“…Note that for quantile regression the loss function is ρ τ false( v false) = v false( τ − I false( v < 0 false) false). 15 One can hardly obtain a similar inequality with (2.4) in Gu and Zou 22 since it cannot be justified as strongly convex or L-smooth, while this will provide a succinct course in the follow-up theoretical study. Although Shan and Yang 21 considered a surrogate of ρ τ false( v false), which is nondifferentiable at v = 0, they only contributed the oracle inequality via the surrogate loss.…”

Section: Methodsmentioning

confidence: 99%

“…In an effort to acquire the asymptotic properties of aggregated estimator, we establish the oracle inequalities under particular risk measures. Since the risk bound under the squared error loss can be hardly derived in quantile regression, (Gu and Zou 22 ), we propose a novel smoothing scheme for the quantile check loss function, which supplies the strong convexity and the L-smoothness. Furthermore, we utilize EAW algorithm to additive mixed effect model and construct the estimation of τ-CQF.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive aggregation for longitudinal quantile regression based on censored history process

Xiong

Deng

Wang

et al. 2023

Stat Methods Med Res

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Most of the studies for longitudinal quantile regression are based on the correct specification. Nevertheless, one specific model can hardly perform precisely under different conditions and assessing which conditions are (approximately) satisfied to determine the optimal one is rather difficult. In the case of the mixed effect model, the misspecification of the fixed effect part will cause a lack of predicting accuracy of random effects, and affect the efficiency of the cumulative function estimator. On the other hand, limited research has focused on incorporating multiple candidate procedures in longitudinal data analysis, which is of current emergency. This paper proposes an exponential aggregation weighting algorithm for longitudinal quantile regression. Based on the secondary smoothing loss function, we establish oracle inequalities for aggregated estimator. The proposed method is applied to evaluate the cumulative [Formula: see text]th quantile function for additive mixed effect model with right-censored history process, and an aggregation-based best linear prediction for random effects is constructed as well. We show that the asymptotic properties are conveniently imposed owing to the smoothing scheme. Simulation studies are carried out to exhibit the rationality, and our method is illustrated to analyze the data set from a multicenter automatic defibrillator implantation trial.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive aggregation for longitudinal quantile regression based on censored history process

Xiong

Deng

Wang

et al. 2023

Stat Methods Med Res

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“…The seminal work of Hansen (2007) has spawned a large recent literature on model averaging. Gu and Zou (2019) recently develop an exponential weighting scheme to construct a model averaging for expectile regressions in fixed dimension. Here, as the number of candidate models to average can diverge with the sample size, we consider a jackknife model averaging (Hansen and Racine, 2012; Lu and Su, 2015, JMA) for expectile regression after screening.…”

Section: Postscreening Model Uncertaintymentioning

confidence: 99%

Variable Screening and Model Averaging for Expectile Regressions

Wang

2023

Oxf Bull Econ Stat

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Expectile regression is a useful tool in modelling data with heterogeneous conditional distributions. This paper introduces two new concepts, i.e. the expectile correlation and expectile partial correlation, which can measure the contribution from each regressor to the response in expectile regression. In ultra-high dimensional setting, the expectile partial correlation, which provides an importance ranking of the predictors, is found useful for variable screening. Theoretical results indicate that the proposed screening procedure can achieve the sure screening set. Additionally, a model selection method via extended Bayesian information criterion (EBIC) and a jackknife model averaging (JMA) method are suggested after the screening step to address model uncertainty. The screening consistency of EBIC, the asymptotic optimality of JMA in the sense of minimizing out-of-sample expectile final prediction error, and the sparsity of JMA weight are then established. Finally, numerical results demonstrate the nice performance of our proposed methods.

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“…We use the data from previous 20 days as predictors, which aims to handle the dependence in the data. The same strategy was used in Gu and Zou (2019) (Riskτ ) to measure model performance of expectile regression model with level τ . The Riskτ is defined as…”

Section: Sp 500 Index Datamentioning

confidence: 99%

“…We use the data from previous 20 days as predictors, which aims to handle the dependence in the data. The same strategy was used in Gu and Zou (2019). On the training set, we fit ER-Boost, KERE, and Expectile NN regression models with each expectile level.…”

Section: Sp 500 Index Datamentioning

confidence: 99%

Expectile regression via deep residual networks

Yin

Zou

2021

Stat

Self Cite

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Expectile is a generalization of the expected value in probability and statistics. In finance and risk management, the expectile is considered to be an important risk measure due to its connection with gain-loss ratio and its coherent and elicitable properties. Linear multiple expectile regression was proposed in 1987 for estimating the conditional expectiles of a response given a set of covariates. Recently, more flexible nonparametric expectile regression models were proposed based on gradient boosting and kernel learning. In this paper, we propose a new nonparametric expectile regression model by adopting the deep residual network learning framework and name it Expectile NN. Extensive numerical studies on simulated and real datasets demonstrate that Expectile NN has very competitive performance compared with existing methods. We explicitly specify the architecture of Expectile NN so that it is easy to be reproduced and used by others. Expectile NN is the first deep learning model for nonparametric expectile regression.

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Aggregated Expectile Regression by Exponential Weighting

Cited by 3 publications

References 34 publications

Adaptive aggregation for longitudinal quantile regression based on censored history process

Adaptive aggregation for longitudinal quantile regression based on censored history process

Variable Screening and Model Averaging for Expectile Regressions

Expectile regression via deep residual networks

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