  In prescriptive analytics, the decision-maker observes historical samples of
$(X, Y)$, where $Y$ is the uncertain problem parameter and $X$ is the
concurrent covariate, without knowing the joint distribution. Given an
additional covariate observation $x$, the goal is to choose a decision $z$
conditional on this observation to minimize the cost $\mathbb{E}[c(z,Y)|X=x]$.
This paper proposes a new distributionally robust approach under Wasserstein
ambiguity sets, in which the nominal distribution of $Y|X=x$ is constructed
based on the Nadaraya-Watson kernel estimator concerning the historical data.
We show that the nominal distribution converges to the actual conditional
distribution under the Wasserstein distance. We establish the out-of-sample
guarantees and the computational tractability of the framework. Through
synthetic and empirical experiments about the newsvendor problem and portfolio
optimization, we demonstrate the strong performance and practical value of the
proposed framework.
