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Erschienen in:
2012 | OriginalPaper | Buchkapitel
6. Prediction of Linear Regression Evaluated Subject to Inequality Constraints on Parameters
verfasst von : Pavel S. Knopov, Arnold S. Korkhin
Erschienen in: Regression Analysis Under A Priori Parameter Restrictions
Verlag: Springer New York
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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.