Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk
TLDR
This paper introduces a distributionally robust, risk-sensitive estimation method using Wasserstein balls and CVaR, solvable via semidefinite programming.
Key contributions
- Proposes a distributionally robust, risk-sensitive estimation framework using Wasserstein ambiguity sets.
- Measures estimator performance using Conditional Value-at-Risk (CVaR) of the squared estimation error.
- Shows affine estimators minimizing worst-case CVaR are solvable via SDP for finitely supported nominal distributions.
- Demonstrates superior out-of-sample CVaR performance on a real-world electricity price forecasting task.
Why it matters
This paper offers a robust way to estimate signals under uncertainty, crucial for applications where risk management is key. By providing a tractable solution, it enables more reliable decision-making in fields like finance and energy. Its practical validation shows real-world applicability.
Original Abstract
We propose a distributionally robust approach to risk-sensitive estimation of an unknown signal x from an observed signal y. The unknown signal and observation are modeled as random vectors whose joint probability distribution is unknown, but assumed to belong to a given type-2 Wasserstein ball of distributions, termed the ambiguity set. The performance of an estimator is measured according to the conditional value-at-risk (CVaR) of the squared estimation error. Within this framework, we study the problem of computing affine estimators that minimize the worst-case CVaR over all distributions in the given ambiguity set. As our main result, we show that, when the nominal distribution at the center of the Wasserstein ball is finitely supported, such estimators can be exactly computed by solving a tractable semidefinite program. We evaluate the proposed estimators on a wholesale electricity price forecasting task using real market data and show that they deliver lower out-of-sample CVaR of squared error compared to existing methods.
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