The present body of knowledge in monotone regression is confined to some isolated existence theorems about point estimation and hypothesis testing. The investigator plans to implement these general methods for as many aspects of regression analysis as possible. In particular, formulas for confidence and prediction intervals will be derived by inverting hypothesis tests, since usual methods are inapplicable because of lack of pivotals. The proposed study will also involve construction of user-oriented tables to bring the restricted procedures to a level comparable to the unrestricted ones. In regression analysis one tries to predict one variable in terms of another. In many applications, especially in social sciences and economics, it is reasonable to assume that the predicted variable tends to increase (or decrease) as the predictor variable increases. Statistical inferences under such assumptions are at a very primitive stage at present, and consist primarily of some general mathematical theorems. The proposed study aims at developing concrete formulas and tables so that users can apply them directly to real-life problems.
