Probability for Statisticians

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Springer Science & Business Media, Jun 9, 2000 - Mathematics - 585 pages
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Probability for Statisticians is intended as a text for a one year graduate course aimed especially at students in statistics. The choice of examples illustrates this intention clearly. The material to be presented in the classroom constitutes a bit more than half the text, and the choices the author makes at the University of Washington in Seattle are spelled out. The rest of the text provides background, offers different routes that could be pursued in the classroom, ad offers additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic funcion presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. The martingale coverage includes coverage of censored data martingales. The text includes measure theoretic preliminaries, from which the authors own course typically includes selected coverage. The author is a professor of Statistics and adjunct professor of Mathematics at the University of Washington in Seattle. He served as chair of the Department of Statistics 1986-- 1989. He received his PhD in Statistics from Stanford University. He is a fellow of the Institute of Mathematical Statistics, and is a former associate editor of the Annals of Statistics.
  

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Contents

IV
1
V
12
VI
18
VII
21
VIII
24
IX
29
X
33
XI
35
LXVI
276
LXVII
279
LXVIII
288
LXIX
292
LXX
295
LXXI
298
LXXII
302
LXXIII
305

XII
37
XIII
40
XIV
44
XV
46
XVI
51
XVII
61
XVIII
66
XIX
70
XX
74
XXI
79
XXII
84
XXIII
86
XXIV
90
XXV
95
XXVI
101
XXVII
104
XXVIII
107
XXIX
110
XXX
111
XXXI
115
XXXII
119
XXXIII
123
XXXIV
127
XXXV
134
XXXVI
137
XXXVII
140
XXXVIII
147
XXXIX
151
XL
155
XLI
157
XLII
158
XLIII
168
XLIV
174
XLV
179
XLVI
187
XLVII
191
XLVIII
199
XLIX
203
L
204
LI
206
LII
210
LIII
215
LIV
223
LV
226
LVI
235
LVII
239
LVIII
241
LIX
246
LX
247
LXI
252
LXII
255
LXIII
264
LXIV
269
LXV
274
LXXIV
308
LXXV
311
LXXVI
314
LXXVII
318
LXXVIII
323
LXXIX
325
LXXX
333
LXXXI
338
LXXXII
341
LXXXIII
346
LXXXIV
350
LXXXV
352
LXXXVI
358
LXXXVII
361
LXXXVIII
363
LXXXIX
365
XC
366
XCI
371
XCII
380
XCIII
383
XCIV
390
XCV
396
XCVI
399
XCVII
407
XCVIII
410
XCIX
412
C
415
CI
416
CII
426
CIII
432
CIV
437
CV
449
CVI
458
CVII
467
CVIII
472
CIX
473
CX
481
CXI
487
CXII
492
CXIII
499
CXIV
501
CXV
511
CXVI
516
CXVII
522
CXVIII
529
CXIX
531
CXX
540
CXXI
546
CXXII
555
CXXIII
563
CXXIV
570
CXXV
575
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About the author (2000)

Galen R. Shorack is a Professor of Statistics at the University of Washington. He is a Fellow of the Institute of Mathematical Statistics and has written a graduate level text on probability theory.

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