Jackknife model averaging for expectile regressions in increasing dimension

Tu, Yundong; Wang, Siwei

doi:10.1016/j.econlet.2020.109607

Cited by 7 publications

(10 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The consistency and asymptotic normality of expectile regression estimator have been initially established by Newey and Powell (1987) for fixed

p

, and recently extended by Tu and Wang (2020) to allow for model misspecification and slowly increasing

p

relative to the sample size

n

.…”

Section: Correlation Measures In Expectile Regressionmentioning

confidence: 99%

“…To determine the averaging weight assigned to each candidate model, we use the leave‐one‐out jackknife criterion adapted from Tu and Wang (2020) as follows. Let

{\overset{bold-italicθ}{true}}_{i, 𝒜} = \arg \min_{{bold-italicθ}_{𝒜}} \frac{1}{n} \sum_{j \neq i} ρ_{τ} false(Y_{j} prefix- {boldX}_{j, 𝒜}^{⊤} {bold-italicθ}_{𝒜} false)

be the leave‐one‐out expectile estimator and define the leave‐one‐out cross‐validation expectile loss function as

C{V}_n\left(\mathbf{w}\right)=\frac{1}{n}\sum \limits_{i=1}^n\kern.3em {\rho}_{\tau}\left({Y}_i-{\tilde{\mu}}_i\left(\mathbf{w}\right)\right),

where

{\overset{μ}{true}}_{i} false(boldw false) = \sum_{k = 0}^{d} w_{k} {boldX}_{i, 𝒜^{false(k false)}}^{⊤} {\overset{bold-italicθ}{true}}_{i, 𝒜^{false(k false)}}

.…”

Section: Postscreening Model Uncertaintymentioning

confidence: 99%

“…For

d=O\left({n}^{\varsigma +2\kappa -\omega}\right),

this assumption implies that

nd\exp \left(-{n}^{1-4\kappa }{\underset{\_}{c}}_n^2\right)=o(1)

and

nd\exp \left(-{n}^{1-4\kappa +\omega -\varsigma }{\underset{\_}{c}}_n^2\right)=o(1)

, relaxing the rate condition in assumption A.3 of Lu and Su (2015) and assumption 3 in Tu and Wang (2020).…”

Section: Postscreening Model Uncertaintymentioning

confidence: 99%

“…It is known in the literature (Hansen, 2007; Hansen and Racine, 2012; Zhang, Wan, and Zou, 2013) that the asymptotic optimality of model averaging requires that there is no finite approximating model for which the model bias is zero (to avoid an asymptotically zero denominator). However, such a requirement is not needed for JMA with the FPE loss (Lu and Su, 2015; Tu and Wang, 2020), as it is always positive by taking into account both parameter estimation error and the model error term.…”

Section: Postscreening Model Uncertaintymentioning

confidence: 99%

“…The extended Bayesian information criterion (EBIC) proposed by Chen and Chen (2008) is adapted to construct a model selection method for expectile regression. In addition, the jackknife model averaging, recently investigated by Tu and Wang (2020), is utilized to obtain more stable expectile forecast after the screening. The theoretical development includes the screening consistency of EBIC, the asymptotic optimality of JMA in terms of minimizing out‐of‐sample expectile final prediction error (FPE) and the weight sparsity of JMA that assigns zero weights to underfitted candidate models.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Variable Screening and Model Averaging for Expectile Regressions

Wang

2023

Oxf Bull Econ Stat

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…The consistency and asymptotic normality of expectile regression estimator have been initially established by Newey and Powell (1987) for fixed

p

, and recently extended by Tu and Wang (2020) to allow for model misspecification and slowly increasing

p

relative to the sample size

n

.…”

Section: Correlation Measures In Expectile Regressionmentioning

confidence: 99%

“…To determine the averaging weight assigned to each candidate model, we use the leave‐one‐out jackknife criterion adapted from Tu and Wang (2020) as follows. Let