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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.
The conjunction of (bio-)chemical recognition elements with nanoscale biological building blocks such as virus particles is considered as a very promising strategy for the creation of biohybrids opening novel opportunities for label-free biosensing. This work presents a new approach for the development of biosensors using tobacco mosaic virus (TMV) nanotubes or coat proteins (CPs) as enzyme nanocarriers. Sensor chips combining an array of Pt electrodes loaded with glucose oxidase (GOD)-modified TMV nanotubes or CP aggregates were used for amperometric detection of glucose as a model system for the first time. The presence of TMV nanotubes or CPs on the sensor surface allows binding of a high amount of precisely positioned enzymes without substantial loss of their activity, and may also ensure accessibility of their active centers for analyte molecules. Specific and efficient immobilization of streptavidin-conjugated GOD ([SA]-GOD) complexes on biotinylated TMV nanotubes or CPs was achieved via bioaffinity binding. These layouts were tested in parallel with glucose sensors with adsorptively immobilized [SA]-GOD, as well as [SA]-GOD crosslinked with glutardialdehyde, and came out to exhibit superior sensor performance. The achieved results underline a great potential of an integration of virus/biomolecule hybrids with electronic transducers for future applications in biosensorics and biochips.