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The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.
Let X₁,…,Xₙ be independent and identically distributed random variables with distribution F. Assuming that there are measurable functions f:R²→R and g:R²→R characterizing a family F of distributions on the Borel sets of R in the way that the random variables f(X₁,X₂),g(X₁,X₂) are independent, if and only if F∈F, we propose to treat the testing problem H:F∈F,K:F∉F by applying a consistent nonparametric independence test to the bivariate sample variables (f(Xᵢ,Xⱼ),g(Xᵢ,Xⱼ)),1⩽i,j⩽n,i≠j. A parametric bootstrap procedure needed to get critical values is shown to work. The consistency of the test is discussed. The power performance of the procedure is compared with that of the classical tests of Kolmogorov–Smirnov and Cramér–von Mises in the special cases where F is the family of gamma distributions or the family of inverse Gaussian distributions.
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 paper deals with the asymptotic behaviour of estimators, statistical tests and confidence intervals for L²-distances to uniformity based on the empirical distribution function, the integrated empirical distribution function and the integrated empirical survival function. Approximations of power functions, confidence intervals for the L²-distances and statistical neighbourhood-of-uniformity validation tests are obtained as main applications. The finite sample behaviour of the procedures is illustrated by a simulation study.
Das Diskussionspapier beschreibt einen Prozess an der FH Aachen zur Entwicklung und Implementierung eines Self-Assessment-Tools für Studiengänge. Dieser Prozess zielte darauf ab, die Relevanz der Themen Digitalisierung, Internationalisierung und Nachhaltigkeit in Studiengängen zu stärken. Durch Workshops und kollaborative Entwicklung mit Studiendekan:innen entstand ein Fragebogen, der zur Reflexion und strategischen Weiterentwicklung der Studiengänge dient.
Background
Minor changes in protein structure induced by small organic and inorganic molecules can result in significant metabolic effects. The effects can be even more profound if the molecular players are chemically active and present in the cell in considerable amounts. The aim of our study was to investigate effects of a nitric oxide donor (spermine NONOate), ATP and sodium/potassium environment on the dynamics of thermal unfolding of human hemoglobin (Hb). The effect of these molecules was examined by means of circular dichroism spectrometry (CD) in the temperature range between 25°C and 70°C. The alpha-helical content of buffered hemoglobin samples (0.1 mg/ml) was estimated via ellipticity change measurements at a heating rate of 1°C/min.
Results
Major results were:
1) spermine NONOate persistently decreased the hemoglobin unfolding temperature T u irrespectively of the Na + /K + environment,
2) ATP instead increased the unfolding temperature by 3°C in both sodium-based and potassium-based buffers and
3) mutual effects of ATP and NO were strongly influenced by particular buffer ionic compositions. Moreover, the presence of potassium facilitated a partial unfolding of alpha-helical structures even at room temperature.
Conclusion
The obtained data might shed more light on molecular mechanisms and biophysics involved in the regulation of protein activity by small solutes in the cell.