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840 Index |
Maximum likelihood estimator Minimize absolute deviations normal equations in, 683, 685, |
(cont.) principle, 477, 679 705-708 |
Cramér-Rao inequality and, 375. Minimum variance unbiased parameters for, 682 |
data sufficiency for, 369 estimator, 341-343, 358, and polynomial regression, |
Fisher information and, 371, 375 369, 375 691-693 |
for geometric distribution Mixed effects model, 593~603 prediction interval in, 689 |
parameter, 742 Mixed exponential distribution, 229 principle of least squares in, |
in goodness-of-fit testing, 733 mle. See Maximum likelihood 683-706 |
in homogeneity test, 745 estimate residuals in, 685, 691, 688, 691, |
in independence test, 748 Mode 708, 713 |
in likelihood ratio tests, 475 of a continuous distribution, squared multiple correlation in, |
in linear regression, 631, 639 228, 229 686, 709 |
in logistic regression, 650 of a data set, 46 sum of squares in, 686, 708-710 |
sample size and, 357 of a discrete distribution, 156 1 ratios in, 690, 712 |
score function and, 377 Model utility test, 647-649 Multiplication rule, 77-88 |
MeNemar’s test, 526, 550 Moment generating function Multiplicative exponential |
Mean of a Bernoulli rv, 122, 127 regression model, 721 |
of Cauchy distribution, 322, of a binomial rv, 135 Multiplicative power regression |
342, 761 of a chi-squared rv, 315 model, 721 |
conditional, 255-257 CLT and, 329-330 Multivariate data, 3, 20 |
correction for the, 560 of a continuous rv, 175-177 Multivariate hypergeometric |
deviations from the, 33, 206, 563, definition of, 122, 175 distribution, 244 |
631, 739 of a discrete rv, 122-127 Mutually exclusive events, 54, 79 |
of a function, 115, 245-246 of an exponential rv, 221 MVUE. See Minimum variance |
vs. median, 28 of a gamma ry, 195 unbiased estimator |
moments about, 121 of a linear combination, 311 |
outliers and, 27, 28 and moments, 124, 176 N |
population, 26 of a negative binomial rv, 143 Negative binomial distribution, |
regression to the, 260, 636 of a normal rv, 191 141-144 |
sample, 25 of a Poisson rv, 149 definition of, 141 |
of sample total, 296 of a sample mean, 329-330 estimation of parameters, 352, 738 |
See also Average uniqueness property of, 123,176 Negative binomial random |
Mean square Moments variable, 141 |
expected, 573, 589, 593, 594, definition of, 121 Newton’s binomial theorem, 143 |
600, 604 method of, 350-352, 358,740 Neyman factorization theorem, 363 |
lack of fit, 681 and moment generating function, | Neyman-Pearson theorem, 470-475 |
pure error, 681 124, 176 Noncentrality parameter, 423, |
Mean square error Monotonic, 221, 353 574, 582 |
definition of, 335 Multimodal histogram, 19 Noncentral f distribution, 423 |
of an estimator, 335 Multinomial distribution, 240,725 Nonhomogeneous Poisson |
MVUE and, 341 Multinomial experiment, 240, 724 process, 156 |
sample size and, 337 Multiple regression Nonstandard normal distribution, |
Measurement error, 337 additive model, 682, 705 185-188 |
Median categorical variables in, 696-699 Normal distribution |
in boxplot, 37-38 coefficient of multiple asymptotic, 298, 371, 375, 377 |
of a distribution, 27, 28 determination, 686, 709 binomial distribution and, |
as estimator, 378, 478 confidence intervals in, 712 189-190, 302 |
vs. mean, 28 covariance matrices in, 711-713 bivariate, 258-260, 310, 318, |
outliers and, 26, 28, 29 degrees of freedom in, 685, 477, 677-671 |
population, 28 696, 708 confidence interval for mean of, |
sample, 27, 271 diagnostic plots, 691 383-388, 392, 398, 403 |
statistic, 378 fitted values in, 685 continuity correction and, 189-190 |
Mendel’s law of inheritance, 726-728 F ratio in, 687, 709 density curves for, 180 |
M-estimator, 359, 381 interaction in models for, 693-698 and discrete random variables, |
Midfourth, 46 leverages in, 714-715 188-190 |
Midrange, 333 logistic regression model, 699 goodness-of-fit test for, 730, 740 |
Mild outlier, 39, 393 in matrix/vector format, 705~715 of linear combination, 309 |
Minimal sufficient statistic, model utility test in, 687, lognormal distribution and, |
366-367, 369 708-709 205, 303 |
--- Trang 854 --- |
Index 841 |
nonstandard, 185-188 estimator for a, 332-346 mean squared error of, 335 |
pdf for, 179 Fisher information on, 371-377 moments method, 350-352, 358 |
percentiles for, 182-188, 210 goodness-of-fit tests for, MVUE of, 340-342, 358, 369, |
probability plot, 210, 740 728-729, 732-736 375 |
Ryan—Joiner test for, 747 hypothesis testing for, 427, 450 notation for, 332, 334 |
standard, 181 location, 217, 367 of a standard deviation and, |
1 distribution and, 320-322, 325, maximum likelihood estimate 286, 340 |
402 of, 354-359, 369 standard error of, 344-346 |
z table, 181-183 moment estimators for, 350-352 of a variance, 334, 339 |
Normal equations, 626, 683, 705 MVUE of, 341-343, 358, Point prediction, 405, 628, 684 |
Normal probability plot, 210, 740 369, 375 Poisson distribution |
Normal random variable, 181 noncentrality, 574 Erlang distribution and, 202 |
Null distribution, 443-444, 760, 780 null value of, 427 expected value, 149, 152 |
Null hypothesis, 426 of a probability distribution, exponential distribution and, 199 |
Null set, 54, 57 103-104 gamma distribution and, 783 |
Null value, 427, 436 in regression, 617-618, 622, goodness-of-fit tests for, 736-738 |
624-636, 658, 666, 682 in hypothesis testing, 470-472, |
o scale, 195, 203, 217-218, 365 474, 482, 550 |
Observational study, 488 shape, 217-218, 365 mode of, 156 |
Odds ratio, 621-622, 750-751 sufficient estimation of, 361-369 moment generating function |
One-sided confidence interval, Pareto diagram, 24 for, 149 |
398-399 Pareto distribution, 170, 178, 226 nonhomogeneous, 156 |
Operating characteristic curve, 137 _ pf. See Probability density function parameter of, 149 |
Ordered categories, 749-751 Percentiles and Poisson process, 149-151, 199 |
Ordered pairs, 66-67 for continuous random variables, variance, 149, 152 |
Order statistics, 271-278, 338, 166-168 Poisson process, 149-151, 194 |
365-367, 478 in hypothesis testing, 458,740 Polynomial regression model, |
sufficiency and, 365-367 in probability plots, 211-216, 740 691-693 |
Outliers sample, 29, 210-211, 216 Pooled f procedures |
in a boxplot, 37-41 of standard normal distribution, and ANOVA, 477, 504-505, 576 |
definition of, 11 182-184, 211-216 vs. Wilcoxon rank-sum |
extreme, 39-41 Permutation, 68, 69, 535-541 procedures, 769 |
leverage and, 714 Permutation test, 535-541 Posterior probability, 79-81, |
mean and, 29, 415-417 PERT analysis, 207 717, 781 |
median and, 29, 37, 415, 417 Plot Power curves, 574-575 |
mild, 39 probability, 210-218, 369, 499, Power function of a test, 473-475, |
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