On minimizing chi-square distances under the hypothesis of homogeneity or independence for a two-way contingency table |
| |
| Affiliation: | 1. Department of Computer Science and Engineering, Delhi Technical Campus, Greater Noida, India;2. Department of Management Studies, G. L. Bajaj Institute of Management and Research, Greater Noida, India;3. Faculty of Engineering & Technology, Jain (Deemed-to-be University), Bengaluru, India;4. Department of CSE, ASET, Amity University Uttar Pradesh, Noida, India;1. Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain;2. Laboratorio Subterráneo de Canfranc, 22880 Canfranc Estación, Spain;3. Max-Planck-Institut für Physik, 80805 München, Germany;1. A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia;2. AGH University of Science and Technology, Cracow, Poland;3. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine;4. Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India;5. Budker Institute for Nuclear Physics, Novosibirsk, Russia;6. California Polytechnic State University, San Luis Obispo, CA, United States;7. Central China Normal University, Wuhan, China;8. Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba;9. Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico;10. Chicago State University, Chicago, IL, United States;11. China Institute of Atomic Energy, Beijing, China;12. Chungbuk National University, Cheongju, Republic of Korea;13. Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia;14. COMSATS University Islamabad, Islamabad, Pakistan;15. Creighton University, Omaha, NE, United States;16. Department of Physics, Aligarh Muslim University, Aligarh, India;17. Department of Physics, Pusan National University, Pusan, Republic of Korea;18. Department of Physics, Sejong University, Seoul, Republic of Korea;19. Department of Physics, University of California, Berkeley, CA, United States;20. Department of Physics, University of Oslo, Oslo, Norway;21. Department of Physics and Technology, University of Bergen, Bergen, Norway;22. Dipartimento di Fisica dell''Università ‘La Sapienza’ and Sezione INFN, Rome, Italy;23. Dipartimento di Fisica dell''Università and Sezione INFN, Cagliari, Italy;24. Dipartimento di Fisica dell''Università and Sezione INFN, Trieste, Italy;25. Dipartimento di Fisica dell''Università and Sezione INFN, Turin, Italy;26. Dipartimento di Fisica e Astronomia dell''Università and Sezione INFN, Bologna, Italy;27. Dipartimento di Fisica e Astronomia dell''Università and Sezione INFN, Catania, Italy;28. Dipartimento di Fisica e Astronomia dell''Università and Sezione INFN, Padova, Italy;29. Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia, Pavia, Italy;30. Dipartimento di Fisica ‘E.R. Caianiello’ dell''Università and Gruppo Collegato INFN, Salerno, Italy;31. Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy;32. Dipartimento di Scienze e Innovazione Tecnologica dell''Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy;33. Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy;34. Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy;35. European Organization for Nuclear Research (CERN), Geneva, Switzerland;36. Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia;37. Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen, Norway;38. Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic;39. Faculty of Science, P.J. Šafárik University, Košice, Slovakia;40. Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany;41. Fudan University, Shanghai, China;42. Gangneung-Wonju National University, Gangneung, Republic of Korea;43. Gauhati University, Department of Physics, Guwahati, India;44. Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany;45. Helsinki Institute of Physics (HIP), Helsinki, Finland;46. High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico;47. Hiroshima University, Hiroshima, Japan;48. Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms, Germany;49. Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania;50. Indian Institute of Technology Bombay (IIT), Mumbai, India;51. Indian Institute of Technology Indore, Indore, India;52. Indonesian Institute of Sciences, Jakarta, Indonesia;53. INFN, Laboratori Nazionali di Frascati, Frascati, Italy;54. INFN, Sezione di Bari, Bari, Italy;55. INFN, Sezione di Bologna, Bologna, Italy;56. INFN, Sezione di Cagliari, Cagliari, Italy;57. INFN, Sezione di Catania, Catania, Italy;58. INFN, Sezione di Padova, Padova, Italy;59. INFN, Sezione di Pavia, Pavia, Italy;60. INFN, Sezione di Roma, Rome, Italy;61. INFN, Sezione di Torino, Turin, Italy;62. INFN, Sezione di Trieste, Trieste, Italy;63. Inha University, Incheon, Republic of Korea;64. Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht, Netherlands;65. Institute for Nuclear Research, Academy of Sciences, Moscow, Russia;66. Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia;67. Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India;68. Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic;69. Institute of Space Science (ISS), Bucharest, Romania;70. Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany;71. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico;72. Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil;73. Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico;74. iThemba LABS, National Research Foundation, Somerset West, South Africa;75. Jeonbuk National University, Jeonju, Republic of Korea;76. Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik und Mathematik, Frankfurt, Germany;77. Joint Institute for Nuclear Research (JINR), Dubna, Russia;78. Korea Institute of Science and Technology Information, Daejeon, Republic of Korea;79. KTO Karatay University, Konya, Turkey;80. Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France;81. Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France;82. Lawrence Berkeley National Laboratory, Berkeley, CA, United States;83. Lund University Department of Physics, Division of Particle Physics, Lund, Sweden;84. Moscow Institute for Physics and Technology, Moscow, Russia;85. Nagasaki Institute of Applied Science, Nagasaki, Japan;86. Nara Women''s University (NWU), Nara, Japan;87. National and Kapodistrian University of Athens, School of Science, Department of Physics, Athens, Greece;88. National Centre for Nuclear Research, Warsaw, Poland;89. National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India;90. National Nuclear Research Center, Baku, Azerbaijan;91. National Research Centre Kurchatov Institute, Moscow, Russia;92. Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark;93. Nikhef, National institute for subatomic physics, Amsterdam, Netherlands;94. NRC Kurchatov Institute IHEP, Protvino, Russia;95. NRC Kurchatov Institute – ITEP, Moscow, Russia;96. NRNU Moscow Engineering Physics Institute, Moscow, Russia;97. Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom;98. Nuclear Physics Institute of the Czech Academy of Sciences, Řež u Prahy, Czech Republic;99. Oak Ridge National Laboratory, Oak Ridge, TN, United States;100. Ohio State University, Columbus, OH, United States;101. Petersburg Nuclear Physics Institute, Gatchina, Russia;102. Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia;103. Physics Department, Panjab University, Chandigarh, India;104. Physics Department, University of Jammu, Jammu, India;105. Physics Department, University of Rajasthan, Jaipur, India;106. Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany;107. Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany;108. Physik Department, Technische Universität München, Munich, Germany;109. Politecnico di Bari and Sezione INFN, Bari, Italy;110. Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany;111. Russian Federal Nuclear Center (VNIIEF), Sarov, Russia;112. Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India;113. School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom;114. Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru;115. St. Petersburg State University, St. Petersburg, Russia;116. Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria;117. SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France;118. Suranaree University of Technology, Nakhon Ratchasima, Thailand;119. Technical University of Košice, Košice, Slovakia;120. The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland;121. The University of Texas at Austin, Austin, TX, United States;122. Universidad Autónoma de Sinaloa, Culiacán, Mexico;123. Universidade de São Paulo (USP), São Paulo, Brazil;124. Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil;125. Universidade Federal do ABC, Santo Andre, Brazil;126. University of Cape Town, Cape Town, South Africa;127. University of Houston, Houston, TX, United States;128. University of Jyväskylä, Jyväskylä, Finland;129. University of Kansas, Lawrence, KS, United States;130. University of Liverpool, Liverpool, United Kingdom;131. University of Science and Technology of China, Hefei, China;132. University of South-Eastern Norway, Tonsberg, Norway;133. University of Tennessee, Knoxville, TN, United States;134. University of the Witwatersrand, Johannesburg, South Africa;135. University of Tokyo, Tokyo, Japan;136. University of Tsukuba, Tsukuba, Japan;137. Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France;138. Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, Lyon, France;139. Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France;140. Université Paris-Saclay Centre d''Etudes de Saclay (CEA), IRFU, Départment de Physique Nucléaire (DPhN), Saclay, France;141. Università degli Studi di Foggia, Foggia, Italy;142. Università di Brescia, Brescia, Italy;143. Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India;144. Warsaw University of Technology, Warsaw, Poland;145. Wayne State University, Detroit, MI, United States;146. Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany;147. Wigner Research Centre for Physics, Budapest, Hungary;148. Yale University, New Haven, CT, United States;149. Yonsei University, Seoul, Republic of Korea;1. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA;2. CCAPP and Department of Physics, The Ohio State University, 191 W. Woodruff Ave., Columbus, OH 43210, USA;3. Department of Astronomy, The Ohio State University, 140 W. 18th Ave., Columbus, OH 43210, USA;1. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoye shosse 31, Moscow 115409, Russia;2. Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, Moscow 117218, Russia;3. Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Moscow Region 141700, Russia;4. University of Kansas, Department of Physics and Astronomy, 1082 Malott Hall, Lawrence, KS 66045, USA |
| |
| Abstract: | The present paper investigates estimation under the hypothesis of homogeneity or independence for a two-way contingency table. A family of optimality criteria (distances) is introduced of which well-known criteria such as maximum likelihood, Pearson- and Neyman chi-square. The Kullback-Liebler distance turn out to be special cases. We look at the convexity properties of this family and provide some general results. Give any member of this family, an analytical solution is provided for the optimal estimator under the hypothesis of homogeneity whereas a simple algorithm solution is given for the optimal row- and column margin estimators under the hypothesis of independence. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
