Functional Data Analysis Method and Its Application
|School||Northeast Normal University|
|Course||Probability Theory and Mathematical Statistics|
|Keywords||Functional data analysis Principal component analysis of the functional Function cluster analysis Statistical depth Permutation test Function discriminant analysis|
Thought of the most essential functional data analysis methods (Functional data analysis, FDA), is regarded the observational data element in the infinite-dimensional function space for processing and analysis. Accompanied by rapid rapid development of the last two decades of science and technology, functional data analysis methods highlights its growing importance in the modern scientific research. Many research fields such as psychology, medical diagnosis, weather forecasting, economics, analysis of children's growth and life sciences, are functional data statistics. Compared with the classic multivariate statistical methods and statistical tools, functional data analysis method is still in its early stage of development, and has a very broad application prospects. Functional data analysis method, there is still a lot of issues that need further research. The main consideration in this article, is a function of data statistical analysis methods and applications, efforts the diverse situations Statistics function method is extended to the case. First, we use of the sparse functional principal component analysis method (Yao et al, 2005) to deal with children with obvious sparsity growth. Through the analysis of the actual data, we found some very interesting conclusions. Second, we will Fraiman-Muniz depth (Fraiman and Muniz, 2001) to promote, constructed several functional depth. At the same time we will multivariate analysis based on the Wilcoxon rank sum test of the depth of the Liu-Singh (Liu and Singh, 1993) extended to the two-sample tests for functional data problem. We choose the function type analysis of variance as well as a comparison method based on the depth of the Wilcoxon rank sum test, through simulation and case study to examine the performance of the test methods mentioned. In recent years, many scholars have begun to use functional data analysis methods for analysis on China's economy, such as Yan Mingyi (2007a, 2007b), Jin Liu, pistil (2008). Chiou and Li (2007) mentioned a function of cluster analysis we also try to take advantage of economic zoning of the various provinces of the country. The clustering results show that this clustering method is feasible, which can provide some reference for similar policymakers. Finally, we sound function and principal components analysis method is proposed based on functional statistical depth function. On this basis, we propose a discriminant analysis method. This method to remove the abnormal values ??may exist discriminant classifier, which is to ensure robust estimates of the unknown parameters. In order to evaluate the performance of the new method, we choose the Lopez-Pintado and Romo (2006b) based on several criterion tape depth as compared. Through simulation studies show that our proposed new method not only misjudge the rate was significantly lower than the comparison method, and save a lot of computing time, and thus worthy of promotion applications.