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REFERENCES
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NOTATION INDEX
C (P) , 251 H(Q,P), 15 Ai (X,S), 86
c ijk (P) , 295 Ai«x,Tl) ,S,r), 404
~* (u) , 214 .F(u) , 202 A (S) , 86
~L (q, 0) , 238 .F*(u) , 214 A(S,r), 404
D(S,r), 409 R, (x) , 14 (i)
m (X,S), 410
DCC, 20 R, I (x) , 15 M(S,r), 4'10
DCCb ' 29 R,(x,S), 86 M, 'k(S,r), 410 ~,J
DCC b ' 29 t(i)(x,S), 86 ].li(x,S,r), 410 ,C
6 (Q;P), 15 L 2 (P) , 15
6(S,r), 412 L* (P) , 15 N(].l,L), 15
L (S) , 86 N a '
15
E:p(on)' 16 L(S,r), 404
LAN, 22 -b 0* (n ), 16
F(X 1 ,Q), 421 L i ' 77
F(S,x 2 ), 421 Li,jk(S), 86 P 172 n
F ' (S,X 2 ), 421 L, 'k(S,r), 404 p 175 ~,J n,u
F'(S,Q), 421 2, 293 &(p) , 60
F P , 14 ~(u) , 202 'I' (P) , 15
<p, 15 2'* (u) , 214 '!' (P), m
98
<I> , 15 2'c ' 293
499
qa (P) , 149 T (P) , 60 n 14 p
Q (x,A), 387 T(p,'ll) , 57 P*f, 15 n -
T1T2 , 77 P ® Q, 15
P (P) , 251 T1xT2 ' 77 Be: , 238
T2 A
Pijk(P) , 294 s '
84 A , 16
T (P) , 251 [a 1 ,···,ak ], 16
Sl:(B) , 239 Tijk(P), 295 f (~) , 15
l:(6,r), 410 7 (~) , 15
AUTHOR INDEX
Akahira, M., 287 Andersen, E.B., 417, 418 Anderson, T.W., 454 Ash, R.B., 80, 81, 94, 456, 481
Bahadur, R.R., 271, 480 Basu, D., 207 Bennett, G., 460 Beran, R., 126, 399 Bhattacharya, R.N., 464, 467,
476 Bickel, P.J., 7, 12, 155, 157,
207, 209, 210, 369, 409, 419, 466
Billingsley, P., 457 Bollmann, M., 397 Boos, D.D., 126,143,147,390 Brown, L.D., 214
Callaert, H., 389 Chibisov, D.M., 12, 155, 157,
173, 335, 342, 394, 395, 397, 461, 466
Clarke, B.R., 140
Das Gupta, S., 453 David, H.A., 390 Deshpande, J.V., 209 Diaconis, P., 396 Dieudonne, J., 63 Doksum, K., 209 Droste, N., 211, 279
Edwards, C.H., 135 Eliseev, V.G., 466
Fabian, V., 369 Falk, M., 444 Feller, W., 467 Filippova, A.A., 126 Freedman, D.A., 396
Godambe, V.P., 418 Gotze, F., 7,17,163,462,
464, 466
Hljek, J., 27, 266, 419 Hannan, J., 369 Hasminskii, R.Z., 369, 406,
407 Helmers, R., 390, 392 Hipp, C., 427 Hu~kovl, H., 24
Ibragimov, LA., 141, 369, 406, 407
389 453
326 326
Janssen, P., Jones, L.E., Juritz, J .M., Juritz, J.W.F.,
Kaigh, W.D., 444 Klaassen, C.A.J., 211, 369 Kochar, S.C., 209
Lachenbruch, P.A., 444 Lambert, D., 95 LeCam, L., 11,22,23,25,27
369
Lehmann, E.L., 206, 207, 209, 210, 213
Levit, B. Ya., 141 Lewis, T., 211 Lindsay, B.G., 409, 418 Loeve, M., 21 Lynch, J., 211
Madansky, A., 247 Mammitzsch, V., 444 Matsuda, T., 461 Michel, R., 394,397,461 Mimmack, G., 211 von Mises, R., Moran, P .A.P.,
126, 137 209
Nadaraya, E.A., 443 Nagaev, S.V., 461
Oosterhoff, J., 24
126 467 461
Parr, W.C., Petrov, V. V. , Pfaff, T., 3, Pfanzagl, J.,
206, 215, 247, 252, 367, 383, 394, 395, 473
3, 173, 185, 197, 216, 217, 225, 255, 285, 295, 385, 386, 393, 407, 453, 454,
Post, R., 287 Proschan, F., 211
501
Rao, C.R., 266 Rao, R.R., 464, 467, 476 Ratinger, T., 24 Reiss, R.-D., 17,393,435,
444, 477, 478 Ri tov, Y., 409 Rothenberg, T.J., 453
Saunders, r.w., 209 Serfling, R.J., 126, 390 Shaked, M., 209, 210 Shibata, Y., 399 Stephens, M.A., 326
Takeuchi, K., 287 Thompson, J.W., 211 Tierney, L., 95
Veraverbeke, N., 389
Wefelmeyer, W., 30,185,197, 211, 215, 217, 279, 367, 385, 453, 454
Wertz, W., 207 Whittle, P., 460 Withers, C.S., Wolfowitz, J.,
126, 127 266
van Zwet, W.R., 7, 12, 24, 155, 157, 466
SUBJECT INDEX*
average length of confidence procedure, 247
bound for concentration of confi
dence bound, 250, 255, 272, 429, 436
for concentration of estimator, 257, 406
for power of test, 161, 162, 173, 176
calibration, 372, 388, 389, 398, 416, 424
canonical gradient, 108, 119 canonical second gradient, 121 concentration, 202, 203, 210;-
215, 220 ---of confidence bound, 282,
355, 443 of estimator, 295, 296, 301,
302, 304, 361, 397, 405, 415
confidence coefficient, 246, 250 confidence procedure, 2~ contrast function, 140--convolution theorem,---216, 279,
281, 407 curvature of path, 65
DCC-differentiable path, 20, 52 DCCb,c-differentiable path~ ~,
45 degen~ate convergence condition,
20, 29 differentiable functional, 105,
114 differentiable path, 18, 20, 25,
26, 29, 45, 54, 55
direction of path, 65 distribution of losses, 202
embedding, 269, 273, 279, 297, 439
estimator, 199
full family, 92
geodesic path, 75 Gini's mean difference, 389 global distance, 67 gradient, ~, lOS; 114
Hellinger distance, 15 Hellinger differentiable path,
~, 52
internal randomization, 378, 426
L-functional, 147, 150, 390 local asymptoti~ormality,
22, 40 local-Uniformity, 266 loss function, 202, 214, 225
maximum likelihood estimator, 383, 398, 399, 404, 423
mean differentiable path, 55 mean unbiased estimator, 206 median unbiased estimator,
205, 217, 254 minimum contrast estimator,
393, 398, 399, 404, 414 minimum-contrast functional,
140, 393, 403, 412 von MTSes functional, 136,
389, 419 ---
* Underlined page numbers refer to definitions.
normaI vector field, 113
parametric family, 86, 128, 146 301, 382, 398
power function 183, 184,
product space, product tangent
of test, 194, 348
77 space,
180,
77
quantile, 141, 149, 262, 428 quasiconvex function, 202, 214
random nuisance parameter, 400, 408
randomized confidence bound, 248 randomized estimator, 199 reparametrization of path, 51, 65,
276 risk, 203, 214, 223, 225
second gradient, 114 second order envelop; power
function, 174, 184, 195
503
similar test, 172 spread order, 209, 234, 262 stochastic expan;ion, 335,
396, 405, 414, 423--canonical component,
353, 365 orthogonal~mponent,
353, 365 strongly differ~iable path,
54
tangent space, 57 tangent vector fi;ld, 110
unbiased, unimodal,
205, 206, 217 453
uniqueness property of second derivative, 69
vector field, 110, 113 weakly differentiable path,
25
LIST OF ERRATA FOR
"CONTRIBUTIONS TO A GENERAL ASYMPTOTIC STATISTICAL THEORY"
Since reference is made to several parts of Vol. I, we
include a list of the more misleading misprints. The authors
are grateful to H.Milbrodt, L.Ruschendorf, and H.Strasser
for sending errata lists.
6.2.8
(1-8)P+P t / 8,g
I a (t ) - a I n
The proof contains a number of easily corrected errors
o -a , n
... r (dn)
1f
(Qa \ f) (x)
(1.6.1), 1.6
1 2(x 1-x 2 )
2 1/2 Q«(Q1- q 2)/P) )
= 00
correct
6.2.18
(1-8)P + 8P / t 8, g
la(t) _al- 1 n
_ (1 _ p (x+ct) ) 1j; (x) p(x)
K E ~ (P)
!'(X i ,Qi)2
••• k(nH (dn)
1f1
(Qe ,r f ) (x)
(1.5.1) I 1.5
1 2 2(X1- X2)
2 1/2 P«(Ql- Q2)/P) )
< 00
96 7
96 9
96 10
121 10
126 9
179 2
186 7
186 6
189 7
1901
199 14
202 14
226 10
226 2
2271
230 13
505
o (Q,P')
<
(1.1.10)
power zero
T(Q,~)
p{ q/p > l+d
sufficiently regular estimator-sequence
(10.2.3)
( -1/4) 0p n
in \ll
R. ( •• ) (. ,6) o
6.2.7
K(K (P» ':L(P)K(K (P»
K (P)
functional K
relations
T (Q6 , r ' Or)
k € * (r) Qe r (dx) , Qe r (dx) ,
open set
q(j)(.,6)
q(·,6)
o
correct
>
(1.1.11)
efficiency zero
T(Q,m ) o
Q{ q/p > l+d
sufficiently regular as. median unbiased estimatorsequence
(10.2.2)
Op(n- 1 / 2 )
in ~
':t{o.) (.,6) o
6.3.1
K(') (K(P)) ':L(P)K(') (K{P»
K (P) )
(n) estimator-sequence K
n€N
realizations
T{Q6,r'O)
k € 2* (r)
Qe,r (dx)
Qe,r (dx)
set of positive Lebesgue measure
q(j) (·,6) + q(o,6)
Lecture Notes in Statistics
Vol. 26: Robust and Nonlinear Time Series Analysis. Proceedings, 1983. Edited by J. Franke, W. Hardie and D. Martin. IX, 286 pages. 1984.
Vol. 27: A. Janssen, H. Milbrodt, H. Strasser, Infinitely Divisible Statistical Experiments. VI, 163 pages. 1985.
Vol. 28: S. Amari, Differential-Geometrical Methods in Statistics. V, 290 pages. 1985.
Vol. 29: Statistics in Ornithology. Edited by 8.J. T. Morgan and P. M. North. XXV, 418 pages. 1985.
Vol. 30: J. Grandell. Stochastic Models of Air Pollutant Concentration. V, 110 pages. 1985.
Vol. 31: J. Pfanzagl, Asymptotic Expansions for General Statistical Models. VII. 505 pages. 1985.
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