Page 675 - Probability and Statistical Inference

652 Index

455 Convex function 152-156
Confidence region 463 Jensen’s inequality 154
Mean vector 463-465 Convolutions 185-187
Multiple comparisons 465-469, Cornish-Fisher expansion 267-268
475-476 F percentage point 269-270
Multivariate F distribution 468-
469 t percentage point 267-268
Multivariate t distribution 466 Correlation coefficient 121
Continuous random variables 23 Confidence interval 563
Continuous uniform distribution 37, Sample correlation 216
38 Tests of hypotheses 560-563
Convergence notions 241 Zero correlation and indepen-
Central limit theorem (CLT) dence 139-141, 171-172
257 Counting rules 16
In distribution or law 253 Combinations 16
In probability 242 Permutations 16
Weak law of large numbers
(WLLN) 241-242 Covariance 119
Convergence results 264-270 Covariance inequality 150; see also
Central limit theorem (CLT) Cauchy-Schwarz inequality
257 Applications 122-123, 368
Sample mean 258 Cramér-Rao lower bound (CRLB)
Sample variance 262 366
Chi-square distribution 264 Attainment 368-369
Dominated convergence Non-attainment 369-371
theorem 274 Non-iid case 374-375
F distribution 265 Cramér-Rao inequality 366
Khinchine’s WLLN 245, 270
Sample variance 251-252 Information 368
Mann-Wald Theorem 261, 275 Minimum variance unbiased
Monotone convergence theo- estimator (MVUE) 369-370
rem 71, 92, 274 Non-iid case 374-375
Multivariate F distribution 279- Sufficiency 375-377
280 Credible interval 478, 488
Multivariate t distribution 279- Contrast with confidence
280 intervals 492-493
Probability density function Highest posterior density (HPD)
F distribution 209-211, 267-
268 489-492
t distribution 207-209, 265- Credible sets 488
266 Critical function 399
Percentage points Critical region 397-399
F distribution 268-270 Cumulative distribution function
t distribution 266-267 (cdf); see Distribution function
Slutsky’s Theorem 257, 260- (df)
263 Curved exponential family 144, 335
Weak law of large numbers
(WLLN) 241-242 D
Weak WLLN 242-244, 270 DeMorgan’s Law 5, 11, 51
Sample variance 251-252, Derivative of integral 29, 30