Statistical prediction plays an important role in many decision processes such as university budgeting (depending on the number of students who will enroll), capital budgeting (depending on the remaining lifetime of a fleet of systems), the needed amount of cash reserves for warranty expenses (depending on the number of warranty returns), and whether a product recall is needed (depending on the number of potentially life-threatening product failures). In statistical inference, likelihood ratios have a long history of use for decision making relating to model parameters (e.g., in evidence-based medicine and forensics). We propose a general prediction method, based on a likelihood ratio (LR) involving both the data and a future random variable. This general approach provides a way to identify prediction interval methods that have excellent statistical properties. For example, if a prediction method can be based on a pivotal quantity, our LR-based method will often identify it. For applications where a pivotal quantity does not exist, the LR-based method provides a procedure with good coverage properties for both continuous or discrete-data prediction applications.
翻译:统计预测在许多决策过程中发挥着重要作用,例如大学预算编制(取决于将入学的学生人数)、资本预算编制(取决于一个系统的剩余寿命)、保证费用所需的现金储备数额(取决于保证回报的数量),以及是否需要产品召回(取决于可能危及生命的产品失灵的数量),在统计推论中,可能性比率在与模型参数(例如循证医学和法医学)有关的决策方面有着悠久的使用历史。我们根据涉及数据和未来随机变量的可能性比率(LR)提出了一个一般预测方法。这一一般方法为确定具有良好统计特性的预测间隔方法提供了一种途径。例如,如果预测方法能够以关键数量为基础,那么我们的基于LR的方法往往会确定它。对于不存在关键数量的应用,基于LR的方法为连续或离散数据预测应用提供了一个具有良好覆盖特性的程序。