We investigate predictive density estimation under the $L^2$ Wasserstein loss for location families and location-scale families. We show that plug-in densities form a complete class and that the Bayesian predictive density is given by the plug-in density with the posterior mean of the location and scale parameters. We provide Bayesian predictive densities that dominate the best equivariant one in normal models.

中文翻译：

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Wasserstein 损失下的预测密度估计

我们研究了在 $L^2$Wasserstein 损失下对位置家族和位置尺度家族的预测密度估计。我们表明插件密度形成一个完整的类，并且贝叶斯预测密度由插件密度与位置和尺度参数的后验均值给出。我们提供的贝叶斯预测密度在正常模型中占主导地位。