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This paper considers a paired data framework and discusses the question of marginal homogeneity of bivariate high-dimensional or functional data. The related testing problem can be endowed into a more general setting for paired random variables taking values in a general Hilbert space. To address this problem, a Cramér–von-Mises type test statistic is applied and a bootstrap procedure is suggested to obtain critical values and finally a consistent test. The desired properties of a bootstrap test can be derived that are asymptotic exactness under the null hypothesis and consistency under alternatives. Simulations show the quality of the test in the finite sample case. A possible application is the comparison of two possibly dependent stock market returns based on functional data. The approach is demonstrated based on historical data for different stock market indices.
We discuss the testing problem of homogeneity of the marginal distributions of a continuous bivariate distribution based on a paired sample with possibly missing components (missing completely at random). Applying the well-known two-sample Crámer–von-Mises distance to the remaining data, we determine the limiting null distribution of our test statistic in this situation. It is seen that a new resampling approach is appropriate for the approximation of the unknown null distribution. We prove that the resulting test asymptotically reaches the significance level and is consistent. Properties of the test under local alternatives are pointed out as well. Simulations investigate the quality of the approximation and the power of the new approach in the finite sample case. As an illustration we apply the test to real data sets.
Testing of a 10 kW diffusive micro-mix combustor for hydrogen-fuelled micro-scale gas turbines
(2007)
Purpose
The most commonly used mobility assessments for screening risk of falls among older adults are rating scales such as the Tinetti performance oriented mobility assessment (POMA). However, its correlation with falls is not always predictable and disadvantages of the scale include difficulty to assess many of the items on a 3-point scale and poor specificity. The purpose of this study was to describe the ability of the new Aachen Mobility and Balance Index (AMBI) to discriminate between subjects with a fall history and subjects without such events in comparison to the Tinetti POMA Scale.
Methods
For this prospective cohort study, 24 participants in the study group and 10 in the control group were selected from a population of patients in our hospital who had met the stringent inclusion criteria. Both groups completed the Tinetti POMA Scale (gait and balance component) and the AMBI (tandem stance, tandem walk, ten-meter-walk-test, sit-to-stand with five repetitions, 360° turns, timed-up-and-go-test and measurement of the dominant hand grip strength). A history of falls and hospitalization in the past year were evaluated retrospectively. The relationships among the mobility tests were examined with Bland–Altmananalysis. Receiver-operated characteristics curves, sensitivity and specificity were calculated.
Results
The study showed a strong negative correlation between the AMBI (17 points max., highest fall risk) and Tinetti POMA Scale (28 points max., lowest fall risk; r = −0.78, p < 0.001) with an excellent discrimination between community-dwelling older people and a younger control group. However, there were no differences in any of the mobility and balance measurements between participants with and without a fall history with equal characteristics in test comparison (AMBI vs. Tinetti POMA Scale: AUC 0.570 vs. 0.598; p = 0.762). The Tinetti POMA Scale (cut-off <20 points) showed a sensitivity of 0.45 and a specificity of 0.69, the AMBI a sensitivity of 0.64 and a specificity of 0.46 (cut-off >5 points).
Conclusion
The AMBI comprises mobility and balance tasks with increasing difficulty as well as a measurement of the dominant hand-grip strength. Its ability to identify fallers was comparable to the Tinetti POMA Scale. However, both measurement sets showed shortcomings in discrimination between fallers and non-fallers based on a self-reported retrospective falls-status.