Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk
This work provides a tractable method for robust estimation under distributional uncertainty, benefiting practitioners in risk-sensitive applications like finance and energy.
The paper proposes a distributionally robust approach to risk-sensitive estimation using conditional value-at-risk (CVaR) and Wasserstein ambiguity sets. It shows that affine estimators minimizing worst-case CVaR can be computed via semidefinite programming when the nominal distribution is finitely supported, and demonstrates lower out-of-sample CVaR on electricity price forecasting.
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.