Prediction of Linear Regression Evaluated Subject to Inequality Constraints on Parameters

Abstract

In this chapter we investigate statistical properties of the prediction in a regression with constraints. This problem is very complicated, since even in the case of linear regression and linear constraints the estimation of parameters is a nonlinear problem. Especially, the problem of interval prediction, i.e., of finding the confidence interval for the estimated value, is highly non-trivial. In Sect. 6.1 the interval prediction is constructed based on the distribution function of the prediction error, whose parameters are the true regression parameter α⁰ and the variance σ² of the noise. Section 6.2 is devoted to the interval prediction based on the conditional distribution function of the prediction error.