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Shorack G.R. — Probability for statisticians

Shorack G.R. — Probability for statisticians

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Название: Probability for statisticians

Автор: Shorack G.R.

Аннотация:

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.

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 586

Добавлена в каталог: 10.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Product, measurable rectangle      79
Product, measure existence      80 82
Projection      105 195 201 449
Projection mappings $\pi_{t_{1},/dots,t_{k}}$       90
Projection U-statistic      450
Projection, conditional expectation      174
Qf      111 123 145 147 231
Qf, order-r      134 136
Qf, standardized class $\mathcal{K}$ bounded by $K_{0}$       140
Qf, Winsorized qf $\tilde{K}$       119 123 140 141 143 145 147
Quadratic form      191 369
Quantile      110 112 282 286
Quantile median      210 280
Random censorship      505
Random sample size      225 285
Random variable (see also rv)      33
Ranks and antiranks      121 172 280 326
Rationals      169 289 300 362 410 476 514
Regression      194 378 463
Regularly varying      145 419
Regularly varying definition: at infinity      138
Regularly varying definition: at zero      137
Regularly varying Karamata theorem      137 139
Regularly varying monotone density theorem      137
Regularly varying qf (see also)      137
Regularly varying, De Haan      139
Regularly varying, uniformly      139
Representation theorem, Kolmogorov for $\mathcal{I}_{2}$       402
Representation theorem, Levy — Khinchin      405 412
Revisualization      186 303
Rv      33
Rv, existence of      27 85 88 92 107
Rv, extended      33
Rv, Rademacher      185 213 242
Rv, random element      90
Rv, random process      90
Rv, random vector      84
Sample covariance      455
Sample mean      120 280
Sample median      121 280
Sample quantiles      282 284
Sample space      20
Sample trimmed mean      120
Sample truncated mean      120
Sample variance      120 189 270 272 278—280 370 451
Sample Winsorized mean      120
Sample Winsorized variance      120
Series      71
Series, three-series theorem      241 244
Series, two-series theorem      241
Set theory      3
Set theory, $\bar{\pi}$ -system      3 6 9 28 153 165 309
Set theory, $\lambda$ -system      9 153
Set theory, $\sigma$ -field      3
Set theory, limsup (liminf)      8 155 204
Set theory, monotone class      3 10 81 170
Set theory, set difference A \ B      3
Set theory, symmetric difference $A\DeltaB$       3
Skewness $\gamma_{1}$ and tail heaviness $\gamma_{2}$       383 454
Skorokhod elementary theorem      52 114 404
Skorokhod embedding (see also)      318
Skorokhod theorem      376 534 542
Slowly varying      124 125 127 137 233 268 269 271 272 419
Space, Borel      169
Space, Hilbert      104 174
Space, inner product      104
Space, measurable      3
Space, measure      4
Space, probability      20 33
Space, sample      20
Space, vector      28 104
Spectral decomposition      191 340
St. Petersburg paradox      221
Stable laws      407 409 410
Stable laws, strictly stable      409 411
Stable laws, symmetric      410
Statistics permutation      428
Statistics, L-statistics      437 441
Statistics, R-statistics      280 329 426 462
Statistics, U-statistics      449 456 481
Statistics, V-statistics      457
Stein's approach to CLTs      255 262 263 458 459
Stirling's formula      186
Stopping time      239 305 311 318 321 469 490 492
Stopping time localizing      511
Strong Markov property      182 239 240 308 409
Subsequences      55 60 288 403 533 538
Subsequences, criterion relating $\rightarrow_{a.e.}$ to $\rightarrow_{\mu}$       31
Sufficient statistic      172 173
Symmetrized rv      210 213 219 244 372
Tail equivalence      143 145
Tail equivalence, CLT      134
Tail equivalence, WLLN      136 219
Theorem correspondence      18 20 27 77 85 107
Theorem, absolute continuity of the integral      42 54
Theorem, Arzela      103 539 541
Theorem, Ascoli      103
Theorem, Bochner      363
Theorem, Caratheodory extension (see also)      10 12
Theorem, Carleman      293
Theorem, Chentsov      538
Theorem, chf (see also this topic)      346
Theorem, continuous mapping      288 534

Theorem, convergence implications      57
Theorem, convergence of types      272 291 408 409 412
Theorem, DCT      41 163
Theorem, de la Vallee Poussin      54 56
Theorem, Donsker      320 338 539
Theorem, Doob      368 487 488 539
Theorem, Dynkin's $\pi-\lambda$       9
Theorem, Egorov      60
Theorem, Esseen's lemma (see also chf)      358
Theorem, Fatou's lemma      40 55 71 163 244 376 404
Theorem, Fubini      10 82 115 116 170
Theorem, fundamental of calculus      76 137 258
Theorem, Gnedenko — Kolmogorov      123 131 232
Theorem, Heine — Borel      17 19 96 110
Theorem, Helly selection      288 291 293 539
Theorem, Helly — Bray      52 56 288 291 403 404
Theorem, Helly — Bray, kinder and gentler      292
Theorem, Hilbert space      105 106
Theorem, Jordan — Hahn      62
Theorem, Karamata      137 139
Theorem, Kolmogorov (see also)      87
Theorem, Kronecker's lemma      205 217 221 253
Theorem, Lebesgue (see also)      64
Theorem, local limit (see also)      380
Theorem, Loeve      60
Theorem, Lusin      60
Theorem, Mann — Wald      52 288 291 369
Theorem, Marcinkiewicz — Zygmund      220 238
Theorem, Mason      329 332 336
Theorem, MCT      40 163
Theorem, mg convergence (see also)      473
Theorem, moment convergence      53 244 289
Theorem, monotone class of Halmos      10 81 170
Theorem, monotone density      137
Theorem, only the zero function      31 43 83 164
Theorem, Polya's lemma      289 291
Theorem, portmanteau      290 532
Theorem, principal axes      191
Theorem, Prohorov      537 539
Theorem, Radon — Nikodym      66 77 158
Theorem, residue      344 345
Theorem, Riemann — Lebesgue lemma      355 359 381 392
Theorem, Riesz      31
Theorem, Riesz — Fischer      51
Theorem, rth mean convergence      238
Theorem, Scheffe      60 380
Theorem, Skorokhod (see also)      114
Theorem, Slutsky      33 34 285 346 376 533
Theorem, smoother realization of a process      93
Theorem, Stein's lemma      256
Theorem, Strassen      235 323 542
Theorem, supporting hyperplane      46 50
Theorem, Taylor      72 352
Theorem, Tonelli      82
Theorem, Ulam      541
Theorem, unconscious statistician      42 67 113 158
Theorem, uniform absolute continuity      54
Theorem, Vitali      218
Theorem, Vitali (see also)      55
Theorem, von Neumann      176
Theorem, Weierstrass approximation      223
Tightness      288 289 350 537 539
topology      95
Topology net      96
Topology product      99
Topology separation      97 100
Topology, base and subbase      95
Topology, boundary      95 100 290
Topology, category      100
Topology, compact      96 100 102
Topology, continuity      98 100
Topology, homeomorphism      97 100
Topology, isometry      100
Topology, locally compact      99 100
Topology, one-point compactification      99
Topology, relative      96 323 508
Triangular array      365 399
Trigonometric identities      340
Trimmed      119
Trimmed fraction      120 417
Trimmed mean      119 416
Truncated      207 218 226 228 235 265
Truncated convergence of types      291
Truncated mean      119 226 228 416
Truncated theorem of types      272
Truncated type      109 291
Uan      283 326 377 399
Uncorrelated      157
Uniformity class      146 419
Upcrossing      473 475 478
Vitali covering      17 70
Vitali theorem      55 60 475 479 498
Waiting time      179 240
Wald's identity      240
Wasserstein distance      114
Wilcoxon statistic      454
Wilson — Hilferty approximation      397
Winsorized      119 207 277
Winsorized fraction      120
Winsorized mean      119 226—228
Winsorized moment      269
Winsorized outside      119 123 127 128 140 141 143 264 266 269 276 416
Winsorized variance      119 123 140 141 143 145 147 232 269—272 276

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