Subject Index
(1−α) level p–content intervals
(β, γ)–upper tolerance limit
F–distributions
M–estimates
P–value
S–method
α–trimmed means
α–similar
α–similar on the boundary
σ-field
σ–finite measure
p–content prediction interval
p–content tolerance intervals
p–quantiles
t–test
absolutely continuous
acceptance probability
admissibility of estimators
algebra
alternative hypothesis
analysis of variance
ancillarity
ancillary statistic
association
asymptotic confidence intervals
asymptotic efficacy of Tn
asymptotic efficiency of MLE
asymptotic variance
asymptotically efficient
asymptotically normal
asymptotically size α test
augmented symmetric functions
autoregressive time–series
average predictive error probability
Bahadur’s theorem
Barndorff–Nielsen p*–formula
Bartlett test
Basu’s theorem
Bayes
Bayes decision function
Bayes equivariant
Bayes factor
Bayes procedures
Bayes theorem
Bayesian analysis
Bayesian approach
Bayesian estimation
Bayesian inference
Bayesian testing
Bernoulli trials
best linear combination of order statistics
best linear unbiased estimators
Beta distributions
beta function
Bhattacharyya lower bound
binomial distribution
bivariate distribution function
Bonferroni inequality
Borel σ–field
Borel–Cantelli Lemma
Box–Muller transformation
C.R. regularity conditions
canonical parameters
Cantelli’s theorem
Cantor distribution
Cauchy distribution
Central Limit Theorem
central moments
Chapman–Robbins inequality
characteristic function
Chebychev inequality
Chebychev–Hermite polynomial
chi–squared distribution
classical Bayesian model
coefficient of correlation
coefficient of determination
coefficient of kurtosis
complete class
complete sufficient statistic
completeness
conditional expectation
conditional probability
conditional test function
confidence interval
confidence level
confidence limits
confidence probability
confidence region
confluent–hypergeometric function
conjugate families
consistency of the MLE
consistent estimators
contingency table
continuity theorem
contrasts
converge in distribution
convergence almost surely
convergence in r–th mean
convergence in distribution
convergence in probability
converges almost–surely
converges in r–th mean
convolution
covariance matrix
covariance stationary
Cramér–Rao lower bound
Cramér–Rao regularity condition
credibility intervals
cross product ratio
cumulants
cumulants generating function
Cumulative Probability Integral Transformation
curved exponential family
decision function
Definition of Sufficiency
degrees of freedom
delta method
DeMorgan’s laws
di–gamma
Dirichlet distribution
discrete algebra
dispersion
distribution free (β, γ) upper tolerance limit
distribution free confidence intervals
distribution free test
distribution of sums
Dominated Convergence Theorem
dynamic linear model
Dynkin’s regularity conditions
Dynkin’s theorem
E–M algorithm
Edgeworth approximation
Edgeworth expansion
efficiency function
efficiency of multi–parameter estimator
empirical Bayes
empirical Bayes estimators
empirical distribution function
equivalent–likelihood partition
equivariant
equivariant estimator
error of Type I
error of Type II
estimating functions
Euler constant
exchangeable
exponential boundedness
exponential conjugate
exponential distribution
exponential integral
exponential type families
exponential type family
extreme value
failure (hazard) rate function
family of distributions
Fatou’s lemma
Fatou’s Theorem
Fieller’s method
Fisher information function
Fisher information matrix
fixed width confidence intervals
formal Bayes estimators
fractiles
Gamma distribution
gamma function
Gauss–Markov Theorem
geometric random
Glivenko–Cantelli’s Theorem
goodness of fit test
guaranteed coverage tolerance intervals
Hardy–Weinberg model
Hellinger distance
Hellinger’s distance
Helmert transformation
hierarchical models
highest posterior density
Holder’s Inequality
Hunt–Stein Theorem
hypergeometric distribution
idempotent matrix
importance density
importance sampling
improper priors
incomplete beta function
incomplete beta function ratio
incomplete gamma function
independence
independent events
information in an estimating function
interaction
interquartile range
Invariance Principle
inverse regression
James–Stein
Jeffreys prior density
Jensen’s Inequality
joint density function
joint distributions
Kalman filter
Karlin’s admissibility theorem
Karlin’s Lemma
Khinchin WLLN
Kullback–Leibler information
kurtosis
Lagrangian
Laplace distribution
Laplace method
large sample confidence intervals
large sample tests
law of iterated logarithm
law of total variance
laws of large numbers
least–squares
least–squares estimators
Lebesgue dominated convergence
Lebesgue integral
likelihood functions
likelihood ratio test
likelihood statistic
Lindeberg–Feller Theorem
linear models
link functions
local hypotheses
location parameter
log–convex
log–normal distribution
log–normal distributions
loss functions
Lyapunov’s Inequality
Lyapunov’s Theorem
main effects
marginal distributions
Markov WLLN
maximal invariant statistic
maximum likelihood estimator
measurable space
median
minimal sufficient statistic
minimax estimators
minimax test
minimum chi–squared estimator
minimum variance unbiased estimator
Minkowsky’s Inequality
mixed effect model
mixture
mixture of the two types
Model II of Analysis of Variance
modes of convergence
moment generating function
moment of order
moment–equations estimators
monotone convergence
monotone likelihood ratio
monotonic class
multinomial distribution
multinormal distribution
multivariate hypergeometric distributions
multivariate negative binomial
multivariate normal distribution
multivariate–t
Negative–Binomial
Newton–Raphson method
Neyman structure
Neyman–Fisher Factorization Theorem
Neyman–Pearson Lemma
non–central F
non–central t
non–central chi–squared
non–informative prior
non–parametric test
normal approximations
normal distribution
normal regression
nuisance parameter
nuisance parameters–unbiased tests
null hypothesis
observed significance level
odds–ratio
operating characteristic function
orbit of
order of magnitude in probability
order statistics
orthogonal subvectors
parameter of non–centrality
parameter space
parametric empirical Bayes
Pareto distribution
partial correlation
partition of sample space
Pascal distribution
Pitman ARE
Pitman estimator
Pitman relative efficiency
Poisson distributions
posterior distribution H(theta | X)
posterior risk
power of a test
pre–test estimators
precision parameter
predictive distributions
predictive error probability
prior distribution
prior risk
probability generating function
probability measure
probability model
proportional–closeness
psi function
Radon–Nikodym
Radon–Nikodym theorem
random sample
random variable
random walk
randomized test
Rao’s efficient score statistic
Rao–Blackwell Lehmann–Scheffé Theorem
rectangular distribution
regression analysis
regular
regular family of distributions
regular parametric family
regularity conditions
regularity conditions for estimating functions
relative betting odds
relative efficiency
ridge regression
ridge trace
Riemann integrable
risk function
robust estimation
saddlepoint approximation
sample correlation
sample median
sample quantile
sample range
scale parameter
Schwarz inequality
score function
second order deficiency
second order efficiency
sensitivity
sequential fixed–width interval estimation
shape parameter
simulation
simultaneous confidence intervals
simultaneous coverage probability
size of a test
skewness
Slutsky’s Theorem
standard deviation
standard normal distribution
standard normal integral
standard–errors
statistic
statistical model
Stein type estimators
Stein’s two–state procedure
Stieltjes–Riemann integral
Stirling approximation
stopping variable
Strong Law of Large Numbers
strongly consistent
structural distributions
structural estimators
student’s t–distribution
subalgebra
sufficient statistics
super efficient
symmetric difference
test function
tetrachoric correlation
The Delta Method
The Law of Total Variance
tight family of distribution
tolerance distributions
tolerance intervals
total life
transformations
trimean
Type I censoring
unbiased estimator
unbiased test
uniform distribution
uniform integrability
uniformly most accurate confidence interval
uniformly most accurate unbiased
uniformly most powerful
upper quartiles
utility function
variance
variance components
variance stabilizing transformation
variance–covariance matrix
Wald Fundamental Identity
Wald Sequential Probability Ratio Test
Wald statistic
Wald Theorem
weak convergence
Weak Law of Large Numbers
Weibull distribution
Weibull distributions
Wiener process
Wilcoxon signed–rank test
Wilks’ likelihood ratio statistic