Unsupervised Self-Normalized Change-Point Testing for Time Series

<p>We propose a new self-normalized method for testing change points in the time series setting. Self-normalization has been celebrated for its ability to avoid direct estimation of the nuisance asymptotic variance and its flexibility of being generalized to handle quantities other than the mean. However, it was developed and mainly studied for constructing confidence intervals for quantities associated with a stationary time series, and its adaptation to change-point testing can be nontrivial as direct implementation can lead to tests with nonmonotonic power. Compared with existing results on using self-normalization in this direction, the current article proposes a new self-normalized change-point test that does not require prespecifying the number of total change points and is thus unsupervised. In addition, we propose a new contrast-based approach in generalizing self-normalized statistics to handle quantities other than the mean, which is specifically tailored for change-point testing. Monte Carlo simulations are presented to illustrate the finite-sample performance of the proposed method. Supplementary materials for this article are available online.</p

The top twenty IPCs in the field of “electrical medical equipment” of oncology.

<p>Note: <i>Coefficient b</i> and <i>P</i> value were obtained from the regression analysis with “the standardized number of patent applications for each year” as the dependent variable and “year” as the independent variable. Bold values refer to the values of subfields with a mean standardized value above (M_<i>max</i> - M_<i>min</i>)/2 or with a significant growing trend (<i>P</i><0.05 and <i>b</i>>0). Italic values refer to the fields whose <i>P</i> values are above 0.05, without statistical significance and their <i>coefficient b</i> values are defined 0 in the two-dimensional quadrant analysis.</p><p>The top twenty IPCs in the field of “electrical medical equipment” of oncology.</p

The top twenty IPCs in the field of “natural products and polymers” of oncology.

<p>Note: <i>Coefficient b</i> and <i>P</i> value were obtained from the regression analysis with “the standardized number of patent applications for each year” as the dependent variable and “year” as the independent variable. Bold values refer to the values of subfields with a mean standardized value above (M_<i>max</i> - M_<i>min</i>)/2 or with a significant growing trend (<i>P</i><0.05 and <i>b</i>>0). Italic values refer to the fields whose <i>P</i> values are above 0.05, without statistical significance and their <i>coefficient b</i> values are defined 0 in the two-dimensional quadrant analysis.</p><p>The top twenty IPCs in the field of “natural products and polymers” of oncology.</p

The key fields of oncology.

<p>The X-axis indicated (M_<i>max</i> - M_<i>min</i>)/2, namely M = 21.89, as cut-off point. The Y-axis indicated the <i>coefficient b</i> in the regression analysis, whose <i>P</i> values of difference-test greater than 0.05, are set as 0 in the figure, and (21.89, 0) was set as the origin of the quadrant.</p

The key technical points in the field of “fermentation industry” of oncology.

<p>The X-axis indicated (M_<i>max</i> - M_<i>min</i>) /2, namely M = 10.21, as cut-off point. The Y-axis indicated the <i>coefficient b</i> in the regression analysis, whose <i>P</i> values of difference-test greater than 0.05, are set as 0 in the figure, and (10.21, 0) was set as the origin of the quadrant.</p

The key technical points in the field of “electrical medical equipment” of oncology.

<p>The X-axis indicated (M_<i>max</i> - M_<i>min</i>) /2, namely M = 8.01, as cut-off point. The Y-axis indicated the <i>coefficient b</i> in the regression analysis, whose <i>P</i> values of difference-test greater than 0.05, are set as 0 in the figure, and (8.01, 0) was set as the origin of the quadrant.</p

Elucidation of hydrogen-release mechanism from methylamine in the presence of borane, alane, diborane, dialane, and borane–alane

<div><p>The mechanisms of hydrogen release from methylamine with or without borane, alane, diborane, dialane, and borane–alane are theoretically explored. Geometries of stationary points are optimised at the MP2/aug-cc-pVDZ level and energy profiles are refined at the CCSD(T)/aug-cc-pVTZ level based on the second-order Møller–Plesset (MP2) optimised geometries. H₂ elimination is impossible from the unimolecular CH₃NH₂ because of a high energy barrier. The results show that all catalysts can facilitate H₂ loss from CH₃NH₂. However, borane or alane has no real catalytic effect because the H₂ release is not preferred as compared with the B–N or Al–N bond cleavage once a corresponding adduct is formed. The diborane, dialane, and borane–alane will lead to a substantial reduction of energy barrier as a bifunctional catalyst. The similar and distinct points among various catalysts are compared. Hydrogen bond and six-membered ring formation are two crucial factors to decrease the energy barriers.</p></div

The key technical points in the field of “diagnosis, surgery” of oncology.

<p>The X-axis indicated (M_<i>max</i> - M_<i>min</i>) /2, namely M = 12.78, as cut-off point. The Y-axis indicated the <i>coefficient b</i> in the regression analysis, whose <i>P</i> values of difference-test greater than 0.05, are set as 0 in the figure, and (12.78, 0) was set as the origin of the quadrant.</p

The key technical points in the field of “natural products and polymers” of oncology.

<p>The X-axis indicated (M_<i>max</i> - M_<i>min</i>)/2, namely M = 11.75, as cut-off point. The Y-axis indicated the <i>coefficient b</i> in the regression analysis, whose <i>P</i> values of difference-test greater than 0.05, are set as 0 in the figure, and (11.75, 0) was set as the origin of the quadrant.</p