The kth power expectile regression

Jiang, Yingying; Lin, Fei; Zhou, Yong

doi:10.1007/s10463-019-00738-y

Cited by 6 publications

(4 citation statements)

References 34 publications

(42 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a generalization of quantiles and expectiles, see M-quantiles in Breckling and Chambers (1988), Koltchinskii (1997), with related consistent scoring functions (Huber quantile scoring functions) defined by Taggart (2022b) while also some intermediate loss functions between the quantile and the expectile losses exist, called kth power expectile losses (Jiang et al 2021).…”

Section: Assessment Of Expectile Predictionsmentioning

confidence: 99%

A review of predictive uncertainty estimation with machine learning

Tyralis,

Papacharalampous

2024

Artif Intell Rev

View full text Add to dashboard Cite

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users’ needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

show abstract

Section: Assessment Of Expectile Predictionsmentioning

confidence: 99%

A review of predictive uncertainty estimation with machine learning

Tyralis,

Papacharalampous

2024

Artif Intell Rev

View full text Add to dashboard Cite

show abstract

“…Compared with ordinary linear regression, in some studies about the weights in child growth, high expenses in medical cost and so on, quantile regression (QR; Koenker & Bassett, 1978) and expectile regression (ER; Newey & Powell, 1987) are preferred by minimizing the asymmetric L 1 and L 2 losses, respectively. To balance robustness and effectiveness, the L p -quantile regression (Hu et al, 2021;Jiang et al, 2021) provides an attractive alternative. Given a fixed 𝜏 ∈ (0, 1), the population L p -quantile of a random variable Y proposed by Chen (1996) is defined as follows:…”

Section: Introductionmentioning

confidence: 99%

{L}^1

and

{L}^2

losses, respectively. To balance robustness and effectiveness, the

{L}^p

‐quantile regression (Hu et al, 2021; Jiang et al, 2021) provides an attractive alternative. Given a fixed

\tau \in \left(0,1\right)

, the population

{L}^p

‐quantile of a random variable

Y

proposed by Chen (1996) is defined as follows:

{Q}_{\tau}\left(Y;p\right)=\underset{v}{\arg\ \min}\kern0.3em \mathrm{E}\left\{{\rho}_{\tau}\left(Y-v;p\right)\right\},

where

{\rho}_{\tau}\left(u;p\right)={\left|\tau -I\left(u<0\right)\Big\Vert u\right|}^p,\kern0.3em p\ge 1,

is the generalized asymmetric

…”

Section: Introductionmentioning

confidence: 99%

Communication‐efficient low‐dimensional parameter estimation and inference for high‐dimensional Lp$$ {L}^p $$‐quantile regression

Gao,

Wang

2023

Scandinavian J Statistics

View full text Add to dashboard Cite

The Lp‐quantile regression generalizes both quantile regression and expectile regression, and has become popular for its robustness and effectiveness especially when 1 < p ≤ 2. In this paper, we consider the data that are inherently distributed and propose two distributed Lp‐quantile regression estimators for a preconceived low‐dimensional parameter in the presence of high‐dimensional extraneous covariates. To handle the impact of high‐dimensional nuisance parameters, we first investigate regularized projection score for estimating low‐dimensional parameter of main interest in Lp‐quantile regression. To deal with the distributed data, we further propose two communication‐efficient surrogate projection score estimators and establish their theoretical properties. The finite‐sample performance of the proposed estimators is studied through simulations and an application to Communities and Crime data set is also presented.This article is protected by copyright. All rights reserved.

show abstract

“…Jiang, Lin, and Zhou [11] propose a method called the kth power expectile regression, which to some extent unifies quantile regression and expectile regression, or generalizes the latter two regression methods. They also point out that under certain conditions, the kth power expectile regression estimate is a maximum likelihood estimate.…”

Section: Introductionmentioning

confidence: 99%

Air Quality Risk Measurement Based on CAViaR Model: A Case Study of PM10 in Beijing

Sun,

Lin

2023

JAMP

Self Cite

View full text Add to dashboard Cite

Air pollution control has always been a global challenge, and significant progress has been made in recent years in controlling air pollutants. However, in some major cities, air pollutant concentrations still exceed the standards. Some scholars have used linear models or conditional autoregressive iterative models to apply the VaR method to predict pollutant concentrations. However, traditional methods based on quantile regression estimation can lead to inadequate risk estimates. Therefore, we propose a method based on the Conditional Autoregressive Value at Risk (CAViaR) model, which uses the kth power expectile regression to estimate VaR. This method does not specify the type of the distribution of data, is easier to calculate the asymptotic variance, more sensitive to extreme values. Applying our method to the data of PM10 in Beijing, we investigate the fitting effects in the case of k = 1, k = 2, and k = 1.9 through predictive tests. The results show that the kth power expectile regression estimates are better than quantile and expectile regression estimates to some extent.

show abstract

The kth power expectile regression

Cited by 6 publications

References 34 publications

A review of predictive uncertainty estimation with machine learning

A review of predictive uncertainty estimation with machine learning

Communication‐efficient low‐dimensional parameter estimation and inference for high‐dimensional Lp$$ {L}^p $$‐quantile regression

Air Quality Risk Measurement Based on CAViaR Model: A Case Study of PM10 in Beijing

Contact Info

Product

Resources

About