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Chentsov's theorem

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166: 176: 171: 25: 37: 65: 60: 33: 17: 8: 108: 55: 29: 143: 118: 44: 91:, Translations of mathematical monographs; v. 191, American Mathematical Society, 81:, Translations of mathematical monographs; v. 53, American Mathematical Society, 148: 131: 122: 160: 99:
Dowty, James G. (2018). "Chentsov's theorem for exponential families".
92: 82: 113: 158: 79:Statistical Decision Rules and Optimal Inference 147: 112: 129: 87:Shun'ichi Amari, Hiroshi Nagaoka (2000) 43:The theorem is named after its inventor 159: 98: 93:http://www.ams.org/books/mmono/191/ 83:http://www.ams.org/books/mmono/053/ 13: 14: 188: 28:is, up to rescaling, the unique 132:"Hommage to Chentsov's theorem" 89:Methods of information geometry 1: 71: 7: 49: 10: 193: 149:10.1007/s41884-022-00077-7 123:10.1007/s41884-018-0006-4 26:Fisher information metric 36:that is invariant under 130:Fujiwara, Akio (2022). 167:Differential geometry 77:N. N. Čencov (1981), 38:sufficient statistics 177:Statistical distance 172:Information geometry 101:Information Geometry 66:Information geometry 61:Sufficient statistic 34:statistical manifold 18:information geometry 56:Fisher information 22:Chentsov's theorem 30:Riemannian metric 184: 153: 151: 126: 116: 45:Nikolai Chentsov 24:states that the 192: 191: 187: 186: 185: 183: 182: 181: 157: 156: 74: 52: 12: 11: 5: 190: 180: 179: 174: 169: 155: 154: 127: 107:(1): 117-135. 96: 85: 73: 70: 69: 68: 63: 58: 51: 48: 9: 6: 4: 3: 2: 189: 178: 175: 173: 170: 168: 165: 164: 162: 150: 145: 141: 137: 133: 128: 124: 120: 115: 110: 106: 102: 97: 95:(Theorem 2.6) 94: 90: 86: 84: 80: 76: 75: 67: 64: 62: 59: 57: 54: 53: 47: 46: 41: 39: 35: 31: 27: 23: 19: 139: 135: 104: 100: 88: 78: 42: 21: 15: 161:Categories 114:1701.08895 72:References 142:: 79–98. 136:Info. Geo 50:See also 109:arXiv 32:on a 144:doi 119:doi 16:In 163:: 138:. 134:. 117:. 103:. 40:. 20:, 152:. 146:: 140:7 125:. 121:: 111:: 105:1

Index

information geometry
Fisher information metric
Riemannian metric
statistical manifold
sufficient statistics
Nikolai Chentsov
Fisher information
Sufficient statistic
Information geometry
http://www.ams.org/books/mmono/053/
http://www.ams.org/books/mmono/191/
arXiv
1701.08895
doi
10.1007/s41884-018-0006-4
"Hommage to Chentsov's theorem"
doi
10.1007/s41884-022-00077-7
Categories
Differential geometry
Information geometry
Statistical distance

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