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In a special paired sample case, Hotelling’s T² test based on the differences of the paired random vectors is the likelihood ratio test for testing the hypothesis that the paired random vectors have the same mean; with respect to a special group of affine linear transformations it is the uniformly most powerful invariant test for the general alternative of a difference in mean. We present an elementary straightforward proof of this result. The likelihood ratio test for testing the hypothesis that the covariance structure is of the assumed special form is derived and discussed. Applications to real data are given.
Hotelling’s T² tests in paired and independent survey samples are compared using the traditional asymptotic efficiency concepts of Hodges–Lehmann, Bahadur and Pitman, as well as through criteria based on the volumes of corresponding confidence regions. Conditions characterizing the superiority of a procedure are given in terms of population canonical correlation type coefficients. Statistical tests for checking these conditions are developed. Test statistics based on the eigenvalues of a symmetrized sample cross-covariance matrix are suggested, as well as test statistics based on sample canonical correlation type coefficients.
Reinigungsprozesse in der Lebensmittelindustrie. Entwicklung eines Demonstrators zur Überwachung
(2017)
Altered neurovascular coupling as measured by optical imaging: a biomarker for Alzheimer’s disease
(2017)
The immobilization of NAD+-dependent dehydrogenases, in combination with a diaphorase, enables the facile development of multiparametric sensing devices. In this work, an amperometric biosensor array for simultaneous determination of ethanol, formate, d- and l-lactate is presented. Enzyme immobilization on platinum thin-film electrodes was realized by chemical cross-linking with glutaraldehyde. The optimization of the sensor performance was investigated with regard to enzyme loading, glutaraldehyde concentration, pH, cofactor concentration and temperature. Under optimal working conditions (potassium phosphate buffer with pH 7.5, 2.5 mmol L-1 NAD+, 2.0 mmol L-1 ferricyanide, 25 °C and 0.4% glutaraldehyde) the linear working range and sensitivity of the four sensor elements was improved. Simultaneous and cross-talk free measurements of four different metabolic parameters were performed successfully. The reliable analytical performance of the biosensor array was demonstrated by application in a clarified sample of inoculum sludge. Thereby, a promising approach for on-site monitoring of fermentation processes is provided.