Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Defining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency)

Bradley Efron
The Annals of Statistics
Vol. 3, No. 6 (Nov., 1975), pp. 1189-1242
Stable URL: http://www.jstor.org/stable/2958246
Page Count: 54
  • Read Online (Free)
  • Download ($19.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Defining the Curvature of a Statistical Problem (with Applications to Second Order Efficiency)
Preview not available

Abstract

Statisticians know that one-parameter exponential families have very nice properties for estimation, testing, and other inference problems. Fundamentally this is because they can be considered to be "straight lines" through the space of all possible probability distributions on the sample space. We consider arbitrary one-parameter families F and try to quantify how nearly "exponential" they are. A quantity called "the statistical curvature of F" is introduced. Statistical curvature is identically zero for exponential families, positive for nonexponential families. Our purpose is to show that families with small curvature enjoy the good properties of exponential families. Large curvature indicates a breakdown of these properties. Statistical curvature turns out to be closely related to Fisher and Rao's theory of second order efficiency.

Page Thumbnails

  • Thumbnail: Page 
1189
    1189
  • Thumbnail: Page 
1190
    1190
  • Thumbnail: Page 
1191
    1191
  • Thumbnail: Page 
1192
    1192
  • Thumbnail: Page 
1193
    1193
  • Thumbnail: Page 
1194
    1194
  • Thumbnail: Page 
1195
    1195
  • Thumbnail: Page 
1196
    1196
  • Thumbnail: Page 
1197
    1197
  • Thumbnail: Page 
1198
    1198
  • Thumbnail: Page 
1199
    1199
  • Thumbnail: Page 
1200
    1200
  • Thumbnail: Page 
1201
    1201
  • Thumbnail: Page 
1202
    1202
  • Thumbnail: Page 
1203
    1203
  • Thumbnail: Page 
1204
    1204
  • Thumbnail: Page 
1205
    1205
  • Thumbnail: Page 
1206
    1206
  • Thumbnail: Page 
1207
    1207
  • Thumbnail: Page 
1208
    1208
  • Thumbnail: Page 
1209
    1209
  • Thumbnail: Page 
1210
    1210
  • Thumbnail: Page 
1211
    1211
  • Thumbnail: Page 
1212
    1212
  • Thumbnail: Page 
1213
    1213
  • Thumbnail: Page 
1214
    1214
  • Thumbnail: Page 
1215
    1215
  • Thumbnail: Page 
1216
    1216
  • Thumbnail: Page 
1217
    1217
  • Thumbnail: Page 
1218
    1218
  • Thumbnail: Page 
1219
    1219
  • Thumbnail: Page 
1220
    1220
  • Thumbnail: Page 
1221
    1221
  • Thumbnail: Page 
1222
    1222
  • Thumbnail: Page 
1223
    1223
  • Thumbnail: Page 
1224
    1224
  • Thumbnail: Page 
1225
    1225
  • Thumbnail: Page 
1226
    1226
  • Thumbnail: Page 
1227
    1227
  • Thumbnail: Page 
1228
    1228
  • Thumbnail: Page 
1229
    1229
  • Thumbnail: Page 
1230
    1230
  • Thumbnail: Page 
1231
    1231
  • Thumbnail: Page 
1232
    1232
  • Thumbnail: Page 
1233
    1233
  • Thumbnail: Page 
1234
    1234
  • Thumbnail: Page 
1235
    1235
  • Thumbnail: Page 
1236
    1236
  • Thumbnail: Page 
1237
    1237
  • Thumbnail: Page 
1238
    1238
  • Thumbnail: Page 
1239
    1239
  • Thumbnail: Page 
1240
    1240
  • Thumbnail: Page 
1241
    1241
  • Thumbnail: Page 
1242
    1242