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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.