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Statistical inference in orthogonal regression for three-part compositional data using a linear model with type-II constraints. (English) Zbl 1270.62097

Summary: Orthogonal regression is a proper tool to analyze relations between two variables when three-part compositional data, i.e., three-part observations carrying relative information (like proportions or percentages), are under examination. When linear statistical models with type-II constraints (constraints involving other parameters besides the ones of the unknown model) are employed for estimating the parameters of the regression line, approximate variances and covariances of the estimated line coefficients can be determined. Moreover, the additional assumption of normality enables to construct confidence domains and perform hypotheses testing. The theoretical results are applied to a real-world example.

MSC:

62J05 Linear regression; mixed models
62F03 Parametric hypothesis testing
62F10 Point estimation
62F25 Parametric tolerance and confidence regions

Software:

alr3
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References:

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