According to the law of likelihood, statistical evidence is represented by likelihood functions and its strength measured by likelihood ratios. This point of view has led to a likelihood paradigm for interpreting statistical evidence, which carefully distinguishes evidence about a parameter from error probabilities and personal belief. Like other paradigms of statistics, the likelihood paradigm faces challenges when data are observed incompletely, due to non-response or censoring, for instance. Standard methods to generate likelihood functions in such circumstances generally require assumptions about the mechanism that governs the incomplete observation of data, assumptions that usually rely on external information and cannot be validated with the observed data. Without reliable external information, the use of untestable assumptions driven by convenience could potentially compromise the interpretability of the resulting likelihood as an objective representation of the observed evidence. This paper proposes a profile likelihood approach for representing and interpreting statistical evidence with incomplete data without imposing untestable assumptions. The proposed approach is based on partial identification and is illustrated with several statistical problems involving missing data or censored data. Numerical examples based on real data are presented to demonstrate the feasibility of the approach.

中文翻译：

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分析可能性和不完整数据

根据似然定律，统计证据用似然函数表示，其强度用似然比来衡量。这种观点导致了解释统计证据的似然范式，它仔细区分了关于参数的证据与错误概率和个人信念。与其他统计范式一样，当数据观察不完整时，可能性范式面临挑战，例如由于无响应或审查。在这种情况下生成似然函数的标准方法通常需要对控制不完整数据观察的机制进行假设，这些假设通常依赖于外部信息并且无法用观察到的数据进行验证。没有可靠的外部信息，使用由便利驱动的不可检验的假设可能会损害作为观察到的证据的客观表示的结果可能性的可解释性。本文提出了一种轮廓似然方法，用于在不强加不可检验的假设的情况下用不完整的数据表示和解释统计证据。所提出的方法基于部分识别，并用涉及缺失数据或删失数据的几个统计问题来说明。给出了基于真实数据的数值例子来证明该方法的可行性。本文提出了一种轮廓似然方法，用于在不强加不可检验的假设的情况下用不完整的数据表示和解释统计证据。所提出的方法基于部分识别，并用涉及缺失数据或删失数据的几个统计问题来说明。给出了基于真实数据的数值例子来证明该方法的可行性。本文提出了一种轮廓似然方法，用于在不强加不可检验的假设的情况下用不完整的数据表示和解释统计证据。所提出的方法基于部分识别，并用涉及缺失数据或删失数据的几个统计问题来说明。给出了基于真实数据的数值例子来证明该方法的可行性。