Predicting a Future Response Using Rank Predictive Probabilities

摘要

Given a vague or partly unspecified relationship between a response variable and an explanatory variable, the problem of predicting a future response is considered. A technique based on the ranks of observations is introduced which uses an approximation to a marginal likelihood of ranks to find predictive probabilities for a future response. The predictive probabilities are defined in terms of the spacings of the order statistics of the sample of responses. Various estimates of the future response based on these probabilities, are considered. Monte Carlo experiments were carried out to compare these new estimates with existing estimates, based on ranks, using isotonic regression and parametric estimates based on Box - Cox transformations. The new estimates perform well.