排列檢定法應用於空間資料之比較

• Main Authors: 王信忠, Wang, Hsin-Chung
• Other Authors: 蔡紋琦
• Format: Thesis
• Language: English
• Published: 2005
• Subjects: 費雪(Fisher)正確檢定; Cramer-von Mises 統計量; 排列檢定; 可交換性; 空間分佈; 貝氏(Bayesian)方法; 檢定力比較; 空間自我迴歸(CAR)模型; auto-Poisson模型; auto-Gaussian模型; 群聚; Fisher`s exact test; Cramer-von Mises statistic; permutation test; exchangeable; spatial distributions; Bayesian approach; power comparison; spatial conditionally autoregressive (CAR) model; auto-Poisson model; auto-Gaussian model; cluster; Alaska fishery research bulletin
• Online Access: https://nccur.lib.nccu.edu.tw//handle/140.119/30930; https://nccur.lib.nccu.edu.tw/bitstream/140.119/30930/1/index.html

博士 國立政治大學 統計研究所 90354503 94 本論文主要是探討在二維度空間上二母體分佈是否一致。我們利用排列\r\n(permutation)檢定方法來做比較, 並藉由費雪(Fisher)正確檢定方法的想法而提出重標記 (relabel)排列檢定方法或稱為費雪排列檢定法。\r\n我們透過可交換性的特質證明它是正確 (exact) 的並且比 Syrjala (1996)所建議的排列檢定方法有更高的檢定力 (power)。\r\n 本論文另提出二個空間模型: spatial multinomial-relative-log-normal 模型 與 spatial Poisson-relative-log-normal 模型\r\n來配適一般在漁業中常有的右斜長尾次數分佈並包含很多0 的空間資料。另外一般物種可能因天性或自然環境因素像食物、溫度等影響而有群聚行為發生, 這二個模型亦可描述出空間資料的群聚現象以做適當的推論。 This thesis proposes the relabel (Fisher`s) permutation test inspired by Fisher`s exact test to compare between distributions of two (fishery) data sets locating on a two-dimensional lattice. We show that the permutation test given by Syrjala (1996} is not exact, but our relabel permutation test is exact and, additionally, more powerful. \r\n This thesis also studies two spatial models: the spatial multinomial-relative-log-normal model and the spatial\r\nPoisson-relative-log-normal model. Both models not only exhibit characteristics of skewness with a long right-hand tail and of high proportion of zero catches which usually appear in fishery data, but also have the ability to describe various types of aggregative behaviors. 1 INTRODUCTION 10\r\n2 SYRJALA’s PERMUTATION TEST 13\r\n2.1 Introduction 13\r\n2.2 Test statistic 17\r\n2.3 Switch permutation is exchangeable? 18\r\n3 SPATIAL MODEL 20\r\n3.1 Model description 21\r\n3.1.1 Conditionally autoregressive model 22\r\n3.1.2 Spatial multinomial-relative-log-normal model 23\r\n3.1.3 Spatial Poisson-relative-log-normal model 24\r\n3.2 Model justification 24\r\n3.2.1 Examples of spatial multinomial-relative-log-normal distribution 26\r\n3.2.2 Examples of spatial Poisson-relative-log-normal distribution 29\r\n3.2.3 Highly skewed with a long right-hand tail 32\r\n4 RELABEL PERMUTATION 35\r\n4.1 Procedure of the relabel permutation 35\r\n4.2 Illustration 36\r\n4.3 Exchangeable 38\r\n4.4 The relabel permutation test 42\r\n5 NUMERICAL ANALYSIS 44\r\n5.1 Simulation design 44\r\n5.2 Size comparison 45\r\n5.3 Power comparison 47\r\n6 CONCLUSION AND ...