State-space model approach to longitudinal data analysis by bootstrap

本研究使用的数据集是由人造卫星（HRDI）和地球上的雷达获得的风速测量数据，范围从80公里到90公里，每1公里，持续14天。我们感兴趣的是检查这两种测量机制之间的显著差异。考虑到数据的依赖性，我们通过以下步骤研究了统计检验问题：(1)在杂类初步数据分析的基础上，构建了三种状态空间模型。(2)将卡尔曼滤波得到的平滑曲线作为初始样本。(3)采用改进的移动块法构造bootstrap样本。(4)通过混合两个样本，我们从零假设中提取bootstrap样本。(5)计算AUC统计量，即两条平滑曲线所包围的面积，然后计算自举分布，并进行统计检验。结果表明：风速受测量高度和日数因素的影响；此外，HRDI测量高估了真实风速。考虑到90 ~ 100km的弱风速区，估计曲线是合理的。接下来，我们推广了这个问题，并测试了两个非平稳数据集（两条曲线）之间的显著差异。提出了8种测试方法，并与传统方法进行了比较。通过对风速数据的模拟研究，对风速的大小和功率进行了检验和比较。检验统计量以AUC为主，但也考虑了平方统计量和绝对差统计量。并对尺度调整的效果进行了考察。结果表明，在大多数情况下，使用AUC的自举检验方法在大小和幂次方面都优于传统方法。

The dataset used in this research is the measurements of wind velocity obtained from an artificial satellite (HRDI), and a rader on the earth, ranging from 80km to 90km at every 1km for 14 days. The interest is to examine the significant difference between these two measuring mechanisms. Considering the dependency of the data, we investigated the statistical testing problem by the following procedure : (1) Based on miscellaneous preliminary data analyses, three kinds of state space models were constructed. (2) Smoothing curves, obtained by the Kalman filter technique, were regarded as an initial sample. (3) Applying a modified moving block method, bootstrap samples were constructed. (4) By mixing the two samples, we made bootstrap samples taken from the null hypothesis. (5) The AUC statistic, which represents the area surrounded by the two smoothing curves, and then the bootstrap distribution were computed, and the statistical testing was carried out. As the result, the following findings were obtained : The wind velocity was affected by measuring altitude and day factors. Also the measurements by HRDI overestimated the true wind velocity. The estimated curves were considered as reasonable, considering the weak wind velocity zone at 90-100km. Next we generalized the problem, and tested the significant difference between two non-stationary dataset (two curves). Eight kinds of testing procedures were proposed, and were compared with some traditional methods. Through simulation sudies based on the wind velocity data, the sizes and powers were examined and compared with each other. As for test statistics, AUC was mainly investigated, however the squared and absolute difference statistics were also taken into consideration. The effect of scale adjustment was also examined. As the result, the proposed bootstrap test using AUC was found to be superior to the traditional methods from the viewpoints of sizes and powers in almost cases.