Robert_V._Hogg,_Joseph_W._McKean,_Allen_T._Craig

Index 739

general scores

regression, 626

likelihood ratio test,seeLikelihood

ratio test

Mann–Whitney–Wilcoxon test, 599

mean

t-test, 272

large sample, 271

large sample, power function, 271

two-sided, large sample, 276

median, 573

Neyman–Pearson Theorem, 472

null hypothesis, 267

observed significance level (p-value),

279

one-sided hypotheses, 275

permutation tests, 310

power, 269

power function, 269

randomized tests, 279

sequential probability ratio test, 502

signed-rank Wilcoxon, 587

significance level, 271

simple hypothesis, 270

size of test, 268

test, 268

two-sided hypotheses, 275

Type I error, 268

Type II error, 268

uniformly most powerful critical re-

gion, 479

uniformly most powerful test, 479

Idempotent, 559
Identity
conditional expectation, 114
iid, 140, 152
Improper prior distributions, 667
Inclusion exclusion formula, 20
Independence
n-variate, 137
expectation, 122
mgf, 122
random variables
bivariate, 118
Independent, 28
events, 28
mutually, 29
Independent and identically distributed,
140
Induced estimator, 570
Inequality
Bonferroni’s inequality, 20
Boole’s inequality, 19
Chebyshev’s, 79
conditional variance, 114
correlation coefficient, 133

Jensen’s, 81

Markov’s, 79

Rao–Cram ́er lower bound, 365

Infimum, 688

Influence function, 641

Hodges–Lehmann estimate, 643

sample mean, 642

sample median, 643

simple linear

LS, 648

Wilcoxon, 648

Instrumental pdf, 298

Interaction parameters, 535

Interquatile range, 52

Intersection, 5

countable intersection, 6

Jacobian, 55

n-variate, 144

bivariate, 102

Jeffreys’ priors, 671

Jeffreys, H., 671

Jensen’s inequality, 81

Johnson, M. E., 496

Johnson, M. M., 496

Joint sufficient statistics, 447

factorization theorem, 447

Jointly complete and sufficient statistics,

449

Jones, M. C., 233

Kendall’sτ, 632

estimator, 632

null properties, 633

Kennedy, W. J., 300, 303

Kernel

rectangular, 233

Kitchens, L.J., 528

Kloke, J. D., 244, 291, 521, 569, 615, 623,

624, 627, 636, 649

Krishnan, T., 404, 409

Kurtosis, 76

Laplace distribution, 77, 106, 260

Law of total probability, 26

Least squares (LS), 541

Lehmann and Scheff ́e theorem, 432

Lehmann, E. L., 233, 277, 334, 383, 386,

389, 393, 398, 423, 452, 457,

487, 488, 594, 614, 676, 679,

681, 682

Leroy, A. M., 627

Likelihood function, 227, 355

Likelihood principle, 417

Likelihood ratio test, 377

asymptotic distribution, 379