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Prediction of Linear Regression Evaluated Subject to Inequality Constraints on Parameters

In: Regression Analysis Under A Priori Parameter Restrictions

Author

Listed:
  • Pavel S. Knopov

    (National Academy of Science of Ukraine)

  • Arnold S. Korkhin

    (National Mining University)

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.

Suggested Citation

  • Pavel S. Knopov & Arnold S. Korkhin, 2012. "Prediction of Linear Regression Evaluated Subject to Inequality Constraints on Parameters," Springer Optimization and Its Applications, in: Regression Analysis Under A Priori Parameter Restrictions, chapter 0, pages 211-221, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0574-0_6
    DOI: 10.1007/978-1-4614-0574-0_6
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