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. 2008 Sep;64(3):931-939.
doi: 10.1111/j.1541-0420.2007.00959.x. Epub 2007 Dec 31.

Order-preserving dimension reduction procedure for the dominance of two mean curves with application to tidal volume curves

Sang Han Lee  1 , Johan Lim  2 , Marina Vannucci  3 , Eva Petkova  4 , Maurice Preter  5 , Donald F Klein  5
Affiliations

Order-preserving dimension reduction procedure for the dominance of two mean curves with application to tidal volume curves

Sang Han Lee et al. Biometrics. 2008 Sep.

Abstract

The paper here presented was motivated by a case study involving high-dimensional and high-frequency tidal volume traces measured during induced panic attacks. The focus was to develop a procedure to determine the significance of whether a mean curve dominates another one. The key idea of the suggested method relies on preserving the order in mean while reducing the dimension of the data. The observed data matrix is projected onto a set of lower rank matrices with a positive constraint. A multivariate testing procedure is then applied in the lower dimension. We use simulated data to illustrate the statistical properties of the proposed testing procedure. Results on the case study confirm the preliminary hypothesis of the investigators and provide critical support to their overall goal of creating an experimental model of the clinical panic attack in normal subjects.

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Figures

Figure 1
Figure 1
Boxplots of MSEs for different values of r, based on 100 generated data sets. The left panel shows the boxplots for p = 10 and the right panel those for p = 100.
Figure 2
Figure 2
The first row shows two sample VT curves after baseline adjustment. The trace in the left panel is an N + L sample, the one in the right panel an S + L. The second row shows the same two curves after wavelet smoothing and the third rowsho ws the corresponding trends.
Figure 3
Figure 3
Mean curves for N + L (line) and S + L (dotted line) after preprocessing. The left panel is for traces after the wavelet smoothing, the right panel is for the trends.
Figure 4
Figure 4
Original (line) and approximated (dotted line) traces for 6 randomly selected subjects. We used r = 25, 4, for smoothed data and trends, respectively. The left panel is for traces after the wavelet smoothing, the right panel is for the trends.
See this image and copyright information in PMC

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