Win-probabilities for regression models
- 作者：A.J. Hayter Anthony.Hayter@du.edu
- 关键词：Multiple linear regression ; Normal distribution ; Confidence interval ; Prediction interval ; Tolerance interval ; Non-central t-distribution ; Normal theory intervals ; One-sided intervals ; Two-sided intervals ; Quantiles ; Cumulative distribution function
- 刊名：Statistical Methodology
- 出版年：2012
- 期刊代码：2_15723127
- 类别：dec
- 出版时间：September, 2012
- 卷：9
- 期：5
- 页码：520-527
- 文件大小：226 K
摘要
This paper considers inferences concerning future observations for regression models. Specifically, the differences between future observations at two designated sets of input values are considered. Win-probabilities, which are the probabilities that one of the future observations will exceed the other, constitute a special case of this analysis. These win-probabilities, together with the more general inferences on the difference between the future observations, provide a useful and easily interpretable tool with which a practitioner can assess the information provided by the regression model, and can make decisions regarding which of the two designated sets of input values would be optimal. A multiple-linear-regression model is considered in detail, although the results can be applied to any regression model with normally distributed errors. Central and non-central -distributions are used for the analysis, and several examples of the methodologies are presented.