Index 745Size of test, 268, 470
Skewed contaminated normal distribution,
494
Skewed distribution, 51
Skewed normal distributions, 197
Skewness, 76
Slutsky’s Theorem, 333
Spearman’s rho, 634
null properties, 635
Spectral decomposition, 200, 557
Spread of a distribution, 52
Square root of positive semi-definite ma-
trix, 200
Standard deviation, 69
Standard error
X, 239
p̂, 241
Standard normal distribution, 187
mean, 188
mgf, 187
variance, 188
Stapleton, J. H., 559
Statistic, 226
Stephens, M. A., 259
Stigler, S. M., 238
Stirling’s formula, 331
Stochastic order, 59
Stromberg, K., 81
Studentized range distribution, 527
Subset, 5
Sufficiency
relation to posterior distribution, 658
Sufficient statistic, 421
Γ(2,θ) distribution, 421
joint,seeJoint sufficient statistics
Lehmann and Scheff ́e theorem, 432
minimal sufficient statistics, 455
Neyman’s factorization theorem, 422
normal
σ^2 known, 423
Rao–Blackwell theorem, 427
relationship to mle, 427
relationship to uniformly most pow-
erful test, 482
shifted exponential distribution, 422
Support, 46
n-variate, 135
continuous random vector, 88
discrete, 46
discrete random vector, 87
Supremum, 688
Swanson, M.R., 528
Terpstra, J. T., 627, 653
Test, 268
t, 272
Theorem
asymptotic normality of mles, 369
Asymptotic Power Lemma, 578
Basu’s theorem, 462
Bayes’ theorem, 26
Boole’s Inequality, 19
Central Limit Theorem, 342
n-variate, 351
Chebyshev’s inequality, 79
Cochran’s Theorem, 566
consistency of mle, 359
continuity theorem of probability, 19
Delta (Δ) method, 335
Jensen’s inequality, 81
Lehmann and Scheff ́e, 432
Markov’s inequality, 79
mle ofg(θ), 358
Neyman’s factorization theorem, 422
Neyman–Pearson, 472
quadratic form
expectation, 556
Rao–Blackwell, 427
Rao–Cram ́er lower bound, 365
Sandwich theorem, 688
Slutsky’s, 333
Student’s theorem, 214
Weak Law of Large Numbers, 322
Tibshirani, R. J., 304, 307, 311
Tolerance interval, 317
Total variation, 206
Trace of a matrix, 555
Transformation, 47
n-variate, 144
not one-to-one, 146
bivariate, 100
continuous, 102
discrete, 100
univariate
continuous, 53, 55
discrete, 47
Translation property, 575
general scores, 610
Mann–Whitney–Wilcoxon, 602
sign process, 575
signed-rank process, 591
Trinomial distribution, 161
Truncated normal distribution, 195
Tucker, H. G., 50, 323, 351
Tukey’s MCP, 527
Tukey, J. W., 258, 259
Tukey-Kramer procedure, 528
Two-sided hypotheses, 275
Two-way ANOVA, 531
additive model, 531
Two-way model, 535
Type I error, 268, 469