Expectile
A distribution summary statistic defined through an asymmetric squared loss, obtained as the minimizer of E[w_τ(Y−θ)²]. It is convex, additive and differentiable, is sensitive to tails, and is used in financial risk measurement.
Timeline (last 90 days)
The paper "Limit Theory for Online Expectile Estimation under Short and Long Range Dependence" provides asymptotic theoretical support for online expectile estimation, covering both short-range and long-range dependence cases.
Expectiles are defined by asymmetrically weighting the squared loss: the solution to minimizing E[w_τ(Y−θ)²] is the τ-expectile, where the weight w_τ is τ when Y>θ and 1−τ otherwise.
Compared with quantiles, expectiles have better mathematical properties (such as additivity and convexity) and show unique advantages in extreme value theory; quantiles as an optimization objective are non-convex and non-additive.
The paper derives the joint long-memory limit across multiple expectile levels and characterizes its limiting covariance structure.
Expectile Value at Risk (EVaR) and conditional expectile are typical applications of expectiles in risk measurement; EVaR can be viewed as a loss measure that weights the tail under an asymmetric squared loss, possesses the good properties of a convex risk measure, and can be efficiently aggregated to the portfolio level through a small number of expectile levels.
All Facts (5)
The paper "Limit Theory for Online Expectile Estimation under Short and Long Range Dependence" provides asymptotic theoretical support for online expectile estimation, covering both short-range and long-range dependence cases.
50%UnverifiedExpectiles are defined by asymmetrically weighting the squared loss: the solution to minimizing E[w_τ(Y−θ)²] is the τ-expectile, where the weight w_τ is τ when Y>θ and 1−τ otherwise.
50%UnverifiedCompared with quantiles, expectiles have better mathematical properties (such as additivity and convexity) and show unique advantages in extreme value theory; quantiles as an optimization objective are non-convex and non-additive.
50%UnverifiedThe paper derives the joint long-memory limit across multiple expectile levels and characterizes its limiting covariance structure.
50%UnverifiedExpectile Value at Risk (EVaR) and conditional expectile are typical applications of expectiles in risk measurement; EVaR can be viewed as a loss measure that weights the tail under an asymmetric squared loss, possesses the good properties of a convex risk measure, and can be efficiently aggregated to the portfolio level through a small number of expectile levels.
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