## Probability for StatisticiansProbability 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 |

570 | |

575 | |

### Common terms and phrases

a-field absolutely continuous arbitrary asymptotic bootstrap Borel sets bounded Brownian bridge Brownian motion called Chapter claim compact condition Consider continuous functions convergence in distribution corollary countable cr-field define Definition denote density df F equal equivalent example Exercise 1.1 exists finite fixed formula gives holds iid rvs implies independent rvs inequality interval Lebesgue measure lemma limit limsup linear martingale matrix mean measurable function measure space metric space monotone Moreover normal notation Note Op(l open sets Poisson probability measures probability space Proof proposition Prove quantile random Recall replace result right continuous s-mg sample satisfies sequence Show signed measure SLLN statistics submg subsets Suppose symmetric theorem 3.1 topology trivial uniform uniformly integrable unique variance vector Verify Winsorized WLLN