Filtering Returns for Unspecified Biases in Priors when Testing Asset Pricing Theory
提出一种方法，在检验资产定价模型时无需假设历史收益分布能一致估计市场先验信念，通过过滤收益率数据中未指定的历史偏差来估计和检验模型，并证明有偏样本也能用于检验模型。
Procedures are presented that allow the empiricist to estimate and test asset pricing models on limited-liability securities without the assumption that the historical payoff distribution provides a consistent estimate of the market's prior beliefs. The procedures effectively filter return data for unspecified historical biases in the market's priors. They do not involve explicit estimation of the market's priors, and hence, economize on parameters. The procedures derive from a new but simple property of Bayesian learning, namely: if the correct likelihood is used, the inverse posterior at the true parameter value forms a martingale process relative to the learner's information filtration augmented with the true parameter value. Application of this central result to tests of asset pricing models requires a deliberate selection bias. Hence, as a by-product, the article establishes that biased samples contain information with which to falsify an asset pricing model or estimate its parameters. These include samples subject to, e.g. survivorship bias or Peso problems.