Statistical Inference under Order Restrictions (The Theory and Application of Isotonic Regression)

Key Points

• This research aims to explore isotonic regression and its applications under order restrictions.
• Developed likelihood ratio tests in the normal case for ordered means.
• Extended and generalized testing strategies for ordered means.
• Utilized isotonic tests to evaluate goodness of fit in statistical models.
• Estimation techniques provided robust results for ordered means under constraints.
• Isotonic tests improved goodness of fit in various applications.
• Demonstrated effectiveness of conditional expectations in sigma-lattices.