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The "curse of dimensionality" problem in Zhou and Wang (2000) can be avoided for a multivariate W. Our approach would at least be useful in cases where the number of variables in Z which are correlated with the missing covariate X is low, whereas the exposure variables of interest and their auxiliary variables may be multivariate.
That is, each of,…, can be regarded as having minimum variance when considered singly, but when considering the vector of effects μ there may be multivariate estimators with smaller variance.
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However, given the selection process that we have described, the distribution of g may not be multivariate normal.
Note that the processes X t,Y t in (5) may be fully multivariate.
(ii) Similar to other copula families (e.g., Archimedean copulas, meta-elliptical copulas, vine copulas, etc)., the MECC may be applied for multivariate analysis in hydrology and water engineering, including multivariate rainfall analysis, multivariate drought analysis, spatial analysis of drainage networks, and spatial analysis of water quality as few examples.
Outliers may be univariate or multivariate.
The chapter will describe examples of process and operational challenges that may be addressed using multivariate analytical approaches then provide guidance on how such approaches can be easily adapted into typical factory environments.
Some of these conflicting results may relate to the interdependency of spectral features and may be clarified by multivariate approaches to statistical dependencies (Anzak et al., 2012).
In order to give a more balanced picture, which reaches over and above the one that may be obtained by multivariate analysis, population attributable fractions were calculated.
Therefore, biofilm structure may be evaluated under multivariate conditions and/or concomitantly with antimicrobial susceptibility testing or other biological assays (Fig. 1).
In general, this can make it harder to identify the (likely few) features that are relevant to determining the phenotype or structure of the system because the desired signal may be buried in multivariate noise.
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CEO of Professional Science Editing for Scientists @ prosciediting.com