740 Index
beta(θ,1) distribution, 381
exponential distribution, 377
for independence, 553
Laplace distribution, 381
multiparameter, 396
asymptotic distribution, 398
multinomial distribution, 398
normal distribution, 396
two-sample normal distribution, 401
variance of normal distribution, 401
normal distribution, mean, 378
relationship to Wald test, 380
two-sample
normal, means, 488
normal, variances, 495, 496
Limit infimum (liminf), 331, 689
Limit supremum (limsup), 331, 689
Linear combinations, 151
Linear discriminant function, 512
Linear model, 540, 645
matrix formulation, 547
simple, 625
Little o notation, 335
Local alternatives, 577, 602
Location and scale distributions, 259
Location and scale invariant statistics,
459
Location family, 364
Location functional, 570
Location model, 242, 571, 572
t-distribution, 217
normal, 191
shift (Δ), 598
Location parameter, 191
Location-invariant statistic, 458
Loggamma distribution, 219
Logistic distribution, 217, 262, 358
Loss function, 414
absolute-error, 416
goalpost, 416
squared-error loss, 416
Lower control limit, 505
Lower fence, 259
Main effect hypotheses, 532
Mann–Whitney–Wilcoxon statistic, 599
Mann–Whitney–Wilcoxon test, 599
null properties, 600
Marginal distribution, 90
continuous, 91
Markov chain, 676
Markov Chain Monte Carlo (MCMC),
680
Markov’s inequality, 79
Marsaglia, G., 297, 303
Maximum likelihood estimator (mle), 226,
227, 357
multiparameter, 387
asymptotic normality, 369
asymptotic representation, 371
binomial distribution, 228
consistency, 359
exponential distribution, 227
logistic distribution, 357
multiparameter
N(μ, σ^2 ) distribution, 387
Laplace distribution, 387
multinomial distribution, 391
Pareto distribution, 394
normal distribution, 228
ofg(θ), 358
one-step, 373
relationship to sufficient statistic, 427
uniform distribution, 230
McKean, J. W., 244, 248, 291, 382, 383,
467, 496, 521, 528, 548, 569,
599, 600, 607, 612, 615, 620,
623–625, 627, 636, 638, 643, 648,
649, 653
McLachlan, G. J., 404, 409
Mean, 61, 68
n-variate, 141
arithmetic mean, 82
conditional, 111
linear identity, 128
geometric mean, 82
grand, 517
harmonic mean, 82
sample mean, 152
Mean profile plots, 531
Median, 51, 76, 572
breakdown point, 645
confidence interval
distribution-free, 262
of a random variable, 51
sample median, 257
Method of moments estimator, 165
mgf,seeMoment generating function
Midrange
sample midrange, 257
Miller, R. G., 529
Minimal sufficient statistics, 455
Minimax criterion, 415
Minimax principle, 415
Minimax test, 509
Minimum chi-square estimates, 286
Minimum mean-squared-error estimator,
415
Minimum variance unbiased estimator,
seeMVUE
Minitab command