On Testing Equal Conditional Predictive Ability Under Measurement Error
研究在预测目标存在测量误差时，如何用损失函数比较不同预测的准确性，发现Bregman类损失函数对测量误差完全稳健，且更精确的代理变量能提高检验区分预测的能力。
Loss functions are widely used to compare several competing forecasts. However, forecast comparisons are often based on mismeasured proxy variables for the true target. We introduce the concept of exact robustness to measurement error for loss functions and fully characterize this class of loss functions as the Bregman class. For such exactly robust loss functions, forecast loss differences are on average unaffected by the use of proxy variables and, thus, inference on conditional predictive ability can be carried out as usual. Moreover, we show that more precise proxies give predictive ability tests higher power in discriminating between competing forecasts. Simulations illustrate the different behavior of exactly robust and non-robust loss functions. An empirical application to US GDP growth rates demonstrates that it is easier to discriminate between forecasts issued at different horizons if a better proxy for GDP growth is used.