Page 679 - Probability and Statistical Inference

656 Index

156, 174-175 Joint confidence region; see Joint
Lyapunov’s 156 confidence intervals
Markov 145 Joint distribution 101, 107-108
Applications 146-149, 173- Joint sufficiency 291-293
174
Tchebysheff’s 148 K
Applications 148-149, 157,
174-175, 243 Karlin-Rubin Theorem 422
Triangular inequality 32 Applications 423-424
Applications 246-247 Khinchine’s WLLN 245
Information 300-304, 540, 563-564 Applications 245, 270-271
Conditional inference 316-318 Sample variance 251-252
Ancillarity 309-311 Kolmogorov axioms 6-7
Inequality; see Cramér-Rao
inequality L
Matrix 305-308
One-parameter case 301-304 Large-sample properties
Recovery of information 312- Maximum likelihood estimator
313, 316 (MLE) 354, 539-542
Sufficiency via information Asymptotic normality 540
303-304 Consistency 540-541
Two-parameter case 305-309 Efficiency 540
Integral Laplace distribution 62, 94, 173
Beta integral 31 Moments 76
By parts 32, 61, 504 Lehmann-Scheffé Theorems 296,
By substitution 39-42, 58, 62- 371
63, 74-76, 82-83, 563 Complete statistic 318-320
Fubini’s Theorem 502 Minimal sufficient statistic 320
Gamma integral 30 323
Invariance property 350 Minimum variance unbiased
Maximum likelihood estimator estimator (UMVUE) 356
(MLE) 345, 539-542 Non-existence 379
Inverse gamma distribution 498-500 Uniqueness 371
Inverse of a matrix 224 Sufficient statistic 320-323
Partitioned matrix 226 Leibnitz’s rule 29, 185
Derivative of integral 29, 30
J Level of a test 399
L’Hôpital’s rule 32
Jacobian of transformation 193- Derivative of integral 32
195, 198 Likelihood function 288, 345, 477,
Jensen’s inequality 154 539
Applications 155-156 Likelihood equation 540
Concave function 152-156 Maximum likelihood estimator
Convex function 152-156 (MLE) 345-350, 539-542
Joint confidence coefficient 451, Minimal sufficiency 294-295,
468-469, 471, 473, 475 300
Joint confidence intervals 451, 468- Neyman factorization 288-289
469, 471, 473, 475 Sufficiency 282, 288-294