| Popis: |
As the number of observation points increase, it is assumed that they are sampled from an underlying real function. Statistical methods that are developed for analyzing this kind of data are called Functional Data Analysis (FDA). The first step in FDA is transforming the random sample, which consists of observations on separate points, into a random sample which consists of real functions. Therefore Basis Function Approach and then Roughness Penalty Approach is used in this study. Since we examined average monthly rainfall and since rainfall data are naturally periodical, Fourier basis functions are utilized. Regularized Functional Principle Components Analysis is used in order to investigate the variation structure in the data. Then the value of the smoothing parameter,, determined by using Generalized Cross-Validation Method. Monthly average rainfall data taken at 71 points from 22 meteorology stations in Aegean Region between 2000 and 2005 are investigated in this study. Firstly, real functions are formed for 22 different stations by using Roughness Penalty Approach. Then, average function, covariance surface, principle component functions, and first principle component derivative function are formed and interpreted.The first principle component function shows that the highest variation between rainfalls occurs in winter months. |
