Page 680 - Probability and Statistical Inference
P. 680
Index 657
Likelihood ratio (LR) 403-413, 416, M
507
Monotone Likelihood ratio Mann-Wald Theorem 261
Applications 262-263, 277-278
property (MLR) 420 Marginal distribution 101-103
Applications 421-424, 434 Markov inequality 145-148
436 Applications 146-148
Test; see Likelihood ratio test Matrix 178, 224-226
Likelihood ratio (LR) test 507 Determinant 224
Bivariate normal distribution Dispersion 214, 218
522 Information matrix 305-308
Comparing means 522-525 Inverse 224
Comparing variances 528- Partitioned 226
529 Jacobian 195-196, 198
Correlation coefficient 525- Negative definite (n.d.) 225-226
528 Non-singular 224
One-sample problem 508 Orthogonal 198, 225
Partitioned 215, 224-226
Normal mean 509-512 Determinant 226
Normal variance 512-515 Inverse 215, 226
Two-sample problem 515 Positive definite (p.d.) matrix
Comparing means 515-518, 225-226
532-533 Positive semi definite (p.s.d.)
Comparing variances 519- matrix 225, 305
522, 533 Rank of a matrix 224
Location family of distributions Maximum likelihood estimator
314-316 (MLE) 345-350, 539-542
Pivotal approach 446-451 Invariance property 350
Confidence interval 446 Large-sample properties
Asymptotic normality 540
Location-scale family of distribu- Consistency 540-541
tions 314-316 Efficiency 540
Pivotal approach 446-451 Median of a distribution 28, 62, 63
Confidence interval 446 Mean squared error 351-354
Logistic distribution 564 Method of moment estimator 342-
Lognormal distribution 45 344
Moment generating function Minimal sufficiency 294-295, 300
(mgf) Basus Theorem 324
Non-existence 95 Complete statistic 320-323
Moments 94 Lehmann-Scheffé Theorems
LHôpitals rule 32 296
Neyman factorization 288-289
Loss function Neyman-Pearson Lemma 402
Squared error loss 352-354, Minimum variance unbiased
579 estimator; see Unbiased estima-
Bayes risk 486 tor
Frequentist Risk 352-354, Moment generating function (mgf)
485-486, 579 79, 254-256
Lyapunovs inequality 156 Determination of a
