An Improved Estimation in Regression Parameter Matrix in Multivariate Regression Model
In: Communications in statistics. Theory and methods, Band 41, Heft 13-14, S. 2305-2320
ISSN: 1532-415X
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In: Communications in statistics. Theory and methods, Band 41, Heft 13-14, S. 2305-2320
ISSN: 1532-415X
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ISSN: 1613-9798
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ISSN: 1547-724X
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ISSN: 1532-415X
In: Statistical papers, Band 50, Heft 1, S. 81-100
ISSN: 1613-9798
In: Statistical papers, Band 65, Heft 4, S. 1985-2009
ISSN: 1613-9798
AbstractWe consider the problem of predicting values of a random process or field satisfying a linear model $$y(x)=\theta ^\top f(x) + \varepsilon (x)$$
y
(
x
)
=
θ
⊤
f
(
x
)
+
ε
(
x
)
, where errors $$\varepsilon (x)$$
ε
(
x
)
are correlated. This is a common problem in kriging, where the case of discrete observations is standard. By focussing on the case of continuous observations, we derive expressions for the best linear unbiased predictors and their mean squared error. Our results are also applicable in the case where the derivatives of the process y are available, and either a response or one of its derivatives need to be predicted. The theoretical results are illustrated by several examples in particular for the popular Matérn 3/2 kernel.
In: CentER Discussion Paper Series Nr. 2021-029
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