Page 676 - Probability and Statistical Inference

Index 653

Leibnitz’s rule 29 Squared error loss 352
Discrete random variables 18 Sufficiency 282, 294-295,
Discrete uniform distribution 37 300
Disjoint sets 5, 6; see also Mutually Two-stage sampling 581-582
exclusive Estimator
Dispersion matrix 214, 218 Bayes 478, 485-487
Distribution; see Probability distri- Best linear unbiased estimator
bution (BLUE) 357-358
Distribution-free confidence Complete; see Complete
interval; see confidence interval statistic
Distribution-free approximate test Confidence interval 441, 569
545-547 Accuracy measures
Location 452-455, 569-571
Sign test 566 Fixed-width 571-574, 584-
Bahadur efficiency 567 587
Mean 543-546 Two-stage sampling
Distribution function (df) 2, 19-20 573-574, 586
Continuity points 25, 56, 57 Consistent 380-382
Continuous case 24, 25 Credible interval 478, 488
Convolutions 185-187 Maximum likelihood estimator
Discontinuity points 24, 25, 26, (MLE) 345, 539-542
56, 57 Asymptotic normality 540
Countable set 26, 27 Consistency 540-541
Discrete case 19, 20, 21, 22 Efficiency 540
Order statistics 182-184 Inconsistency 541
Invariance property 350
Right continuous 22
Dominated convergence theorem Method of moment 342-345
Minimum variance unbiased
274
Double exponential distribution; see estimator; see Uniformly
minimum variance unbiased
Laplace distribution estimator (UMVUE) 341
E Rao-Blackwellization; see Rao-
Blackwellized estimator
Estimation Rao-Blackwellized estimator
Bayes 478, 485-487, 489-492 360-365, 372
Maximum likelihood estimator Rao-Blackwell Theorem 359
(MLE) 345-350, 539-542 Risk function 579
Invariance property 350 Bounded risk 580
Moments estimator 342-344 Squared error loss 352
Point estimation 341 Sufficient; see Sufficiency and
Bayes risk 478, 485-487 Sufficient statistic
Bias 351 Unbiased estimator 351
Bounded risk 579-580, 587- Non-existence 353-354
589 Uniformly minimum variance
Lehmann-Scheffé Theorems unbiased estimator (UMVUE)
296, 371 356
Mean square error 352 Non-existence 379
Risk function 352 Under incompleteness 377-