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Published in:
2012 | OriginalPaper | Chapter
1. Estimation of Regression Model Parameters with Specific Constraints
Authors : Pavel S. Knopov, Arnold S. Korkhin
Published in: Regression Analysis Under A Priori Parameter Restrictions
Publisher: Springer New York
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Abstract
Consider the regression where y
t
∈ℜ
1 is the dependent variable, x
t
∈ℜ
q
is an argument (regressor), α0∈ℜ
n
is a true regression parameter (unknown), \(\tilde{f}({\mathbf{x}}_{t},\alpha )\) is some (nonlinear) function of α, ε
t
is a noise, and t is an observation number.
$${y}_{t} =\tilde{ f}({\mathbf{x}}_{t},{\alpha }^{0}) + {\epsilon }_{ t},\quad t = 1,2,\ldots,$$
(1.1)