Metholds Of Functional Data Analysis And Case Studies

In many fields,the observed data will display an obvious functional feature in the data space. Most of them are smooth curves or continuous functions. In functional data analysis, we consider the observed functional data as a whole, not a series of numbers. It is substantial distinction between method of functional data analysis and traditional statistical analysis. Functional data analysis has the common purposes with traditional statistical analysis.In this paper,we construct a more perfect, systemic theoretical framework about methods of functional data analysis. And we applied method of functional data analysis in new fields. What we mainly research in our paper are listed in blow:1. Choice of basis function. It is the most important method of smoothing discrete data by base function expansion. We used Fourier basis functions, Bernstein basis functions, B-spline functions commonly in base function expansion and we compared their respective advantages and disadvantages in their application fields in this paper. The main work in this paper are that we constructed some other basis functions. Also pointed out that the non-uniform rational B-spline functions to overcome traditional base function cannot exactly describe the curve volatility faults. Triangular basis functions provides a more extensive area of thought. Mixed Bezier class basis functions retain advantages of rational B-spline functions of advantages, but making computation much easier. Thus generating function curves with greater flexibility, get better results.2. Generated functional data curve of smooth processing. Penalty function method is one of the traditional method of smoothing functional data curves. In this paper we give the theory and method of minimizing energy of smoothing curves. And based on the B-spline functions premise, we research the local energy optimal smoothing method, we pick out energy smoothing method based on the curvature homogenization of B-spline curve, non-uniform spline curve smoothing method and stratified energy smoothing method.3.Research on methods of curve analysis. First,we perfect functional data of variance analysis, canonical correlation analysis.Then.we focus on methods of principal components data, making a comprehensive research and empirical analysis. This paper another innovation points is derived based on first Euclidean distance clustering of some conclusion, and Pearson similarity coefficient be introduced in clustering analysis. We define a method of weighted piecewise clustering analysis, the concept of not only master data curve clusters simple local morphological characteristics and improved clustering quality.4. In case studies of functional data analysis, we probe a new way of using functional data analysis. We analysis prices transfer effect before and after RMB exchange rate.We applied methods of functional data analysis into the economic field, and empirical analysis is carried out conclusions. We study the individual handwriting based on functional data analysis.We get extract data characteristic curve, then build up good fitting properties of dynamic model, giveing some useful conclusions about handwriting identification. At last,we use method of functional data analysis applying to the pork price index of seasons change, the study found that the pork price index of the seasons change present cycle changes characteristics. And by analyzing the pork price index major fluctuations,we find out stable interval of pork price index. According to the analysis result,we give some policy suggestions.