排列檢定法應用於空間資料之比較

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-rela...

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Bibliographic Details
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
id ftchengchi:oai:nccur.lib.nccu.edu.tw:140.119/30930
record_format openpolar
institution Open Polar
collection National Chengchi University Institutional Repository (NCCUIR)
op_collection_id ftchengchi
language English
topic 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
spellingShingle 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
王信忠
Wang, Hsin-Chung
排列檢定法應用於空間資料之比較
topic_facet 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
description 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 ...
author2 蔡紋琦
format Thesis
author 王信忠
Wang, Hsin-Chung
author_facet 王信忠
Wang, Hsin-Chung
author_sort 王信忠
title 排列檢定法應用於空間資料之比較
title_short 排列檢定法應用於空間資料之比較
title_full 排列檢定法應用於空間資料之比較
title_fullStr 排列檢定法應用於空間資料之比較
title_full_unstemmed 排列檢定法應用於空間資料之比較
title_sort 排列檢定法應用於空間資料之比較
publishDate 2005
url https://nccur.lib.nccu.edu.tw//handle/140.119/30930
https://nccur.lib.nccu.edu.tw/bitstream/140.119/30930/1/index.html
genre Alaska fishery research bulletin
genre_facet Alaska fishery research bulletin
op_relation Aitchison, J. and Ho, C. H. (1989), “The multivariate Poisson-log normal distribution.”,Biometrika, 76, 643–653.
Anderson, T.W. (1962), “On the distribution of the Two-ample Cramer-von Mises Crite-rion.”, The Annals of mathematical Statistics, 33, 1148–1159.
Anderson, T.W. and Darling, D.A. (1952), “Asymptotic Theory of Certain ”Goodness of Fit” Criteria Based on Stochastic Processes.”, The Annals of Mathematical Statistics,23, 193–212.
Armistead, C.E. and Nichol, D.G. (1993), “1990 Bottom trawl survey of the eastern Bering Sea continental shelf.”, United States Department of Commerce,NOAA Technical Mem-orandum NMFS-AFSC-7.
Besag, J.E. (1974), “Spatial interaction and statistical analysis of lattice systems.”, Journal of the Royal Society B, 36, 192–225.
Brodeur, R.D., Sugisaki, H., and Hunt, G. L. (2002), “Increases in jellyfish biomas in the bering sea: implications for the ecosystem.”, Marine Ecology Process Series ., 233,89–103.
Conover, W.J. (1999), Practical Nonparametric Statistic. Third edition, Wiley, New York.
Cressie, N. (1993), Statistics for Spatial Data, Revised Edition., Wiley, New York.
Cui, H. (2002), “The average projection type weighted cramer-von mises statistics for testing some distribution.”, Science in China (ser. A), 45(5), 562–577.
Deluis, M., Raventos, J., Gonzalez-Hidalgo, J.C., Sanchez, J.R., and Cortina, J. (2000), “Spatial analysis of rainfall trends in the region of valencia (east spain).”, Int. J. Clima-tol., 20, 1451–1469.
Edgington, E.S. (1980), Randomization tests. Second edition., Marcel-Dekker, New York.
Fisz, M. (1960), “On a Result by M.Rosenblatt Concerning the Von Mises-Smirnov Test.”, The Annals of Mathematical Statistics, 31, 427–429.
Good, P. (2000), A practical guide to resampling methods for testing hypotheses. Second edition., Spring-Verlag, New York.
Hedger, R., McKenzie, E., Heath, M., Wright, P., Scott, B., Gallego, A., and Andrews, J. (2004), “Analysis of the spatial distributions of mature cod (gadus morhua) and haddock (melanogrammus aeglefinus) abundance in the north sea (1980-1999) using generalised additive models.”, Fisheries Research., 70, 17–25.
Leach, M.K. and Givnish, T.J. (1999), “Gradients in the composition, structure, and di-versity of remnant oak savannas in southern wisconsin.”, Ecological Monograph., 69,353–374.
Lehmann, E.L. (1986), Testing Statistical Hypotheses.Second Edition, Spring-Verlag, New York.
Pearson, K. (1900), “On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.”, Philosophy Magazine, 50, 157–172.
Swain, D.P. and Wade, E.J. (2003), “Spatial distribution of catch and effort in a fishery for snow crab (Chionoecetes opilio): tests of predictions of the ideal free distribution.”,Can J. Fish. Aquat. Sci., 60, 897–909.
Syrjala, S.E. (1996), “A statistical test for a difference between the spatial distribution of two populations”, Ecology, 77(1), 75–80.
Terceiro, M. (2003), “The statistical properties of recreational catch rate data for some fish stocks off the northeast U.S. coast.”, NMFS Scientific Publications Office.Fish Bull.,101, 653–672.
Wilks, S.S. (1938), “The large-sample distribution of the likelihood ratio for testing com-posite hypotheses.”, Annals of Mathematical Statistics, 9, 60–62.
Wilson, C.D, Hollowed, A.B., Shima, M., Walline, P., and Stienessen, S. (2003), “In-teractions between commercial fishing and walleye pollock.”, Alaska Fishery Research
Bulletin., 10, 61–77.62
G0903545031
https://nccur.lib.nccu.edu.tw//handle/140.119/30930
https://nccur.lib.nccu.edu.tw/bitstream/140.119/30930/1/index.html
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spelling ftchengchi:oai:nccur.lib.nccu.edu.tw:140.119/30930 2024-09-15T17:35:31+00:00 排列檢定法應用於空間資料之比較 Permutation test on spatial comparison 王信忠 Wang, Hsin-Chung 蔡紋琦 2005 https://nccur.lib.nccu.edu.tw//handle/140.119/30930 https://nccur.lib.nccu.edu.tw/bitstream/140.119/30930/1/index.html en_US eng Aitchison, J. and Ho, C. H. (1989), “The multivariate Poisson-log normal distribution.”,Biometrika, 76, 643–653. Anderson, T.W. (1962), “On the distribution of the Two-ample Cramer-von Mises Crite-rion.”, The Annals of mathematical Statistics, 33, 1148–1159. Anderson, T.W. and Darling, D.A. (1952), “Asymptotic Theory of Certain ”Goodness of Fit” Criteria Based on Stochastic Processes.”, The Annals of Mathematical Statistics,23, 193–212. Armistead, C.E. and Nichol, D.G. (1993), “1990 Bottom trawl survey of the eastern Bering Sea continental shelf.”, United States Department of Commerce,NOAA Technical Mem-orandum NMFS-AFSC-7. Besag, J.E. (1974), “Spatial interaction and statistical analysis of lattice systems.”, Journal of the Royal Society B, 36, 192–225. Brodeur, R.D., Sugisaki, H., and Hunt, G. L. (2002), “Increases in jellyfish biomas in the bering sea: implications for the ecosystem.”, Marine Ecology Process Series ., 233,89–103. Conover, W.J. (1999), Practical Nonparametric Statistic. Third edition, Wiley, New York. Cressie, N. (1993), Statistics for Spatial Data, Revised Edition., Wiley, New York. Cui, H. (2002), “The average projection type weighted cramer-von mises statistics for testing some distribution.”, Science in China (ser. A), 45(5), 562–577. Deluis, M., Raventos, J., Gonzalez-Hidalgo, J.C., Sanchez, J.R., and Cortina, J. (2000), “Spatial analysis of rainfall trends in the region of valencia (east spain).”, Int. J. Clima-tol., 20, 1451–1469. Edgington, E.S. (1980), Randomization tests. Second edition., Marcel-Dekker, New York. Fisz, M. (1960), “On a Result by M.Rosenblatt Concerning the Von Mises-Smirnov Test.”, The Annals of Mathematical Statistics, 31, 427–429. Good, P. (2000), A practical guide to resampling methods for testing hypotheses. Second edition., Spring-Verlag, New York. Hedger, R., McKenzie, E., Heath, M., Wright, P., Scott, B., Gallego, A., and Andrews, J. (2004), “Analysis of the spatial distributions of mature cod (gadus morhua) and haddock (melanogrammus aeglefinus) abundance in the north sea (1980-1999) using generalised additive models.”, Fisheries Research., 70, 17–25. Leach, M.K. and Givnish, T.J. (1999), “Gradients in the composition, structure, and di-versity of remnant oak savannas in southern wisconsin.”, Ecological Monograph., 69,353–374. Lehmann, E.L. (1986), Testing Statistical Hypotheses.Second Edition, Spring-Verlag, New York. Pearson, K. (1900), “On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.”, Philosophy Magazine, 50, 157–172. Swain, D.P. and Wade, E.J. (2003), “Spatial distribution of catch and effort in a fishery for snow crab (Chionoecetes opilio): tests of predictions of the ideal free distribution.”,Can J. Fish. Aquat. Sci., 60, 897–909. Syrjala, S.E. (1996), “A statistical test for a difference between the spatial distribution of two populations”, Ecology, 77(1), 75–80. Terceiro, M. (2003), “The statistical properties of recreational catch rate data for some fish stocks off the northeast U.S. coast.”, NMFS Scientific Publications Office.Fish Bull.,101, 653–672. Wilks, S.S. (1938), “The large-sample distribution of the likelihood ratio for testing com-posite hypotheses.”, Annals of Mathematical Statistics, 9, 60–62. Wilson, C.D, Hollowed, A.B., Shima, M., Walline, P., and Stienessen, S. (2003), “In-teractions between commercial fishing and walleye pollock.”, Alaska Fishery Research Bulletin., 10, 61–77.62 G0903545031 https://nccur.lib.nccu.edu.tw//handle/140.119/30930 https://nccur.lib.nccu.edu.tw/bitstream/140.119/30930/1/index.html 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 thesis 2005 ftchengchi 2024-08-05T14:55:17Z 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 ... Thesis Alaska fishery research bulletin National Chengchi University Institutional Repository (NCCUIR)

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