Prediction using non-parametric techniques: some comparisons

Abstract

The prediction of future untransformed responses when the data can be transformed to a linear model is considered but it is assumed that the transformation is unknown.A technique, based on ranks of observations which uses an approximation to a marginal likelihood of ranks to find predictive probabilities for a future response, is introduced.The predictive probabilities are defined in terms of the spacings of the order statistics of the sample of responses.An estimate of the future response, based on these probabilities, is considered.Results of Monte Carlo experiments are given to compare this estimate with existing estimates, based on ranks, using isotonic regression, and parametric estimates based on Box-Cox transformations.The new estimate performs best amongst the group of non-parametric estimators considered and has an efficiency of about 70 per cent compared to the optimal parametric estimator.

Keywords:

• Box-Cox transformation
• isotonic regression
• linear model
• predictive probability
• ranks
• simulation