SUBJECT INDEX
- Absolutely continuous df
- Actions
- Admissible decision rule
- Analysis of variance
- one-way
- table
- two-way
- two-way with interaction
- Ancillary statistic
- Assignment of probability
- equally likely
- on finite sample spaces
- random
- uniform
- Asymptotic distribution,
- of rth order-statistic
- of sample moments
- of sample quantile
- Asymptotic relative efficiency(Pitman’s)
- Asymptotically efficient estimator
- Asymptotically normal
- Asymptotically normal estimator
- best
- consistent
- Asymptotically unbiased estimator
- At random
- Banach’s matchbox problem
- Bayes,
- risk
- rule
- solution
- Behrens-Fisher problem
- Welch approximation
- Bernoulli random variable
- Bernoulli trials
- Bertrand’s paradox
- Best asymptotically normal estimator
- Beta distribution
- bivariate
- MGF
- moments
- Beta function
- Bias of an estimator
- Biased estimator
- Binomial coefficient
- Binomial distribution
- bounds for tail probability
- central term
- characterization
- generalized to multinomial
- Kurtosis
- mean
- MGF
- moments
- PGF
- relation to negative binomial
- tail probability as incomplete beta function
- variance
- Blackwell-Rao theorem
- Bonferroni’s inequality
- Boole’s inequality
- Bootstrap,
- method
- sample
- Borel-Cantelli lemma
- Borel-measurable functions, of an rv
- Buffon’s needle problem
- Canonical form
- Cauchy distribution
- bivariate
- characterization
- characteristic function
- mean does not exist
- MGF does not exist
- moments
- as ratio of two normal
- as stable distribution
- Cauchy-Schwarz inequality
- Central limit theorem
- applications of
- Chapman, Robbins and Kiefer inequality
- for discrete uniform
- for normal
- for uniform
- Characteristic function
- of multiple RVs
- properties
- Chebychev-Bienayme inequality
- Chebychev’s inequality
- improvement of
- Chi-square distribution, central
-
- MGF
- moments
- as square of normal
- noncentral
- MGF
- moments
-
- Chi-square test(s)
- as a goodness of fit
- for homogeneity
- for independence
- one-tailed
- robustness
- for testing equality of proportions
- for testing parameters of multinomial
- for testing variance
- two-tailed
- Combinatorics
- Complete, family of distributions
- Complete families, binomial
- chi-square
- discrete uniform
- hypergeometric
- uniform
- Complete sufficient statistic
- for Bernoulli
- for exponential family
- for normal
- for uniform
- Concordance
- Conditional, DF
- distribution
- PMF
- probability
- Conditional expectation
- properties of
- Confidence, bounds
- coefficient
- estimation problem
- Confidence interval
- Bayesian
- equivariant
- expected length of
- general method(s) of construction
- level of
- length of
- percentile
- for location parameter
- for the parameter of, Bernoulli
- discrete uniform
- exponential
- normal
- uniform
- for quantile of order p
- shortest-length
- from tests of hypotheses
- UMA family
- UMAU family
- for normal mean
- for normal variance
- unbiased
- using Chebychev’s inequality
- using CLT
- using properties of MLE’s
- Conjugate prior distribution
- natural
- Confidence set
- for mean and variance of normal
- UMA family of
- UMAU family of
- unbiased
- Consistent estimator
- asymptotically normal
- in rth mean
- strong and weak
- Contaminated normal
- Contingency table
- Continuity correction
- Continuity theorem
- Continuous type distributions
- Convergence, a.s.
- in distribution = weak
- in law
- of MGFs,
- modes of
- of moments
- of PDFs
- of PMFs
- in probability
- in rth mean
- Convolution of DFs
- Correlation
- Correlation coefficient
- properties
- Countable additivity
- Covariance
- sample
- Coverage, elementary
- r-coverage
- probability
- Credible sets
- Critical region
- Decision function
- Degenerate RV
- Degrees of freedom when pooling classes
- Delta method
- Density function, probability
- Design matrix
- Diachotomous trials
- Discordance
- Discrete distributions
- Discrete uniform distribution
- Dispersion matrix = variance – covariance matrix
- Distribution, conditional
- conjugate prior
- of a function of an RV
- induced
- a posteriori
- a priori
- of sample mean
- of sample median
- of sample quantile
- of sample range
- Distribution function
- continuity points of a
- of a continuous type RV
- convolution
- decomposition of a
- discontinuity points of a
- of a discrete type RV
- of a function of an RV
- of an RV
- of multiple RVs
- Domain of attraction
- Efficiency of an estimate
- relative
- Empirical DF = sample DF
- Equal likelihood
- Equivalent RVs
- Estimable function
- Estimable parameter
- degree
- kernel
- Estimator
- equivariant
- Hodges-Lehmann
- least squares
- minimum risk equivariant
- Pitman
- point
- Event
- ertain,
- elementary = simple
- disjoint = mutually exclusive
- independent
- null
- Exchangeable random variables
- Expectation, conditional
- properties
- Expected value = mean = mathematical expectation
- of a function of RV
- of product of RVs
- of sum of RVs
- Exponential distribution
- characterizations
- memoryless property of
- MGF
- moments
- Exponential family
-
- k-parameter
- natural parameters of
- one-parameter
-
- Extreme value distribution
- Factorial moments
- Factorization criterion
- Finite mixture density function
- Finite population correction
- Fisher Information
- Fisher’s Z-statistic
- Fitting of distribution, binomial
- geometric
- normal
- Poisson
- Fréchet, Cramér, and Rao inequality
- Fréchet, Cramér, and Rao lower bound
- binomial
- exponential
- normal
- one-parameter exponential family
- Poisson
- Fréchet, Cramér, and Rao lower bound
- F-distribution, central
-
- moments of
- noncentral
- moments of
-
- F-test(s)
- of general linear hypothesis
- as generalized likelihood ratio test
- for testing equality of variances
- Gamma distribution
- bivariate
- characterizations
- MGF
- moments
- relation with Poisson
- Gamma function
- General linear hypothesis
- canonical form
- estimation in
- GLR test of
- General linear model
- Generalized Likelihood ratio test
- asymptotic distribution
- F-test as
- for general linear hypothesis
- for parameter of, binomial
- for simple vs. simple hypothesis
- bivariate normal
- discrete uniform
- exponential
- normal
- Generating functions
- moment
- probability
- Geometric distribution
- characterizations
- memoryless property of
- MGF
- moments
- order statistic
- PGF
- Glivenko-Cantelli theorem
- Goodness-of-fit problem
- Hazard(=failure rate) function
- Helmert orthogonal matrix
- Hodges-Lehmann estimators
- Holder’s inequality
- Hypergeometric distribution
- bivariate
- mean and variance
- Hypothesis, tests of
- alternative
- composite
- null
- parametric
- simple
- tests of
- Identically distributed RVs
- Implication rule
- Inadmissible decision rule
- Independence and correlation
- Independence of events
- complete = mutual
- pairwise
- Independence of RVs,
- complete = mutual
- pairwise
- Independent, identically distributed rv’s
- sequence of
- Indicator function
- Induced distribution
- Infinitely often
- Interections
- Invariance, of hypothesis testing problem
- principle
- Invariant,
- decision problem
- family of distributions
- function
- location
- location-scale
- loss function
- maximal
- scale
- statistic
- Invariant, class of distributions
- estimators
- maximal
- tests
- Inverse Gaussian PDF
- Jackknife
- Joint, DF
- PMF
- Jump
- Jump point, ofa DF
- Kendall’s sample tau
- distribution of
- generating function
- Kendall’s tau coefficient
- Kendall’s tau test
- Kernel, symmetric
- Kolmogorov’s, inequality
- strong law of large numbers
- Kolmogorov-Smirnov one sample statistic
- for confidence bounds of DF
- distribution
- Kolmogorov-Smirnov test
- comparison with chi-square test
- one-sample
- two-sample
- Kolmogorov-Smirnov two sample statistic
- distribution
- Kronecker lemma
- Kurtosis, coefficient of
- Laplace = double exponential distribution
- MGF
- Least square estimation
- principle
- restricted
- L’Hospital rule
- Likelihood,
- equal
- equation
- equivalent
- function
- Limit, inferior
- set
- superior
- Lindeberg central limit theorem
- Lindeberg-Levy CLT
- Lindeberg condition
- Linear combinations of RVs
- mean and variance
- Linear dependence
- Linear model
- Linear regression model
- confidence intervals
- estimation
- testing of hypotheses
- Locally most powerful test
- Location family
- Location-scale family
- Logistic distribution
- Logistic function
- Logistic regression
- Lognormal distribution
- Loss function
- Lower bound for variance, Chapman,
- Robbins and Kiefer inequality
- Fréchet, Cramér and Rao inequality
- Lyapunov condition
- Lyapunov inequality
- Maclaurin expansion of an mgf
- Mann-Whitney statistic
- moments
- null distribution
- Mann-Whitney-Wilcoxon test
- Marginal,
- DF
- PMF
- Markov’s inequality
- Maximal invariant statistic
- function of
- Maximum likelihood estimation, principle of
- Maximum likelihood estimator
- asymptotic normality
- consistency
- as a function of sufficient statistic
- invariance property
- Maximum likelihood estimation method applied to, Bernoulli
- binomial
- bivariate normal
- Cauchy
- discrete uniform
- exponential
- gamma
- hypergeometric
- normal
- Poisson
- uniform
- Mean square error
- Median
- Median test
- Memoryless property,
- of exponential
- of geometric
- Method of finding distribution,
- CF orMGF
- DF
- transformations
- Methods of finding confidence interval
- Bayes
- for large samples
- pivot
- test inversion
- Method of moments
- applied to, beta
- binomial
- gamma
- lognormal
- normal
- Poisson
- uniform
- applied to, beta
- Minimal sufficient statistic
- for beta
- for gamma
- for geometric
- for normal
- for Poisson
- for uniform
- Minimax, estimator
- principle
- solution
- Minimax estimation for parameter of,
- Bernoulli
- binomial
- hypergeometric
- Minimum mean square error estimator
- for variance of normal
- Minimum risk equivariant estinator
- for location parameter
- for scale parameter
- Mixing proportions
- Minkowski inequality
- Mixture density function
- Moment, about origin
- absolute
- central
- condition
- Factorial
- of conditional distribution
- of DF
- of functions of multiple RVs
- inequalities
- lemma
- non-existence of order
- of sample covariance
- of sample mean
- of sample variance
- Moment generating function
- continuity theorem for
- differentiation
- existence
- expansion
- limiting
- of linear combinations
- and moments
- of multiple RVs
- of sample mean
- series expansion
- of sum of independent RVs
- uniqueness
- Monotone likelihood ratio
- for hypergeometric
- for one-parameter exponential family
- UMP test for families with
- for uniform
- Most efficient estimator
- asymptotically
- as MLE
- Most powerful test
- for families with MLR
- as a function of sufficient statistic
- invariant
- Neyman-Pearson
- similar
- unbiased
- uniformly
- Multidimentional RV = multiple RV
- Multinomial coefficient
- Multinomial distribution
- MGF
- moments
- Multiple RV
- continuous type
- discrete type
- functions of
- Multiple regression
- Multiplication rule
- Multivariate hypergeometric distribution
- Multivariate negative binomial
- distribution
- Multivariate normal
- dispersion matrix
- Natural parameters
- Negative binomial (=Pascal or waiting time) distribution,
- bivariate
- central term
- mean and variance
- MGF
- Negative hypergeometric distribution
- mean and variance
- Neyman-Pearson lemma
- Neyman-Pearson lemma applied to,
- Bernoulli
- normal
- Noncentral, chi-square distribution
- F-distribution
- t-distribution
- Noncentrality parameter, of chi-square
- F-distribution
- t-distribution
- Noninformative prior
- Nonparametric = distribution-free estimation,
- methods
- Nonparametric unbiased estimation
- of population mean
- of population variance
- Normal approximation, to binomial
- to Poisson
- Normal distribution = Gaussian law
- bivariate
- characteristic function
- characterizations
- contaminated
- folded
- as limit of binomial
- as limit of chi-square
- as limit of Poisson
- MGF
- moments,
- multivariate
- singular
- as stable distribution
- standard
- Normal distribution = Gaussian law (cont’d)
- tail probability
- truncated
- Normal equations
- Odds
- Order statistic
- is complete and sufficient
- joint PDF
- joint marginal PDF
- kth
- marginal PDF
- uses
- moments
- Ordered samples
- Orders of magnitude, o and O notation
- Parameter(s), of a distribution
- estimable
- location
- location-scale
- order
- scale
- shape
- space
- Parametric statistical hypothesis
- alternative
- composite
- null
- problem of testing
- simple
- Parametric statistical inference
- Pareto distribution
- Partition
- coarser
- finer
- minimal sufficient
- reduction of a
- sets
- sub-
- sufficient
- Percentile confidence interval
- centered percentile confidence interval
- Permutation
- Pitman estimator
- location
- scale
- Pitman’s asymptotic relative efficiency
- Pivot
- Point estimator
- Point estimation, problem of
- Poisson DF, as incomplete gamma
- Poisson distribution
- central term
- characterizations
- coefficient of skewness
- kurtosis
- as limit of binomial
- as limit of negative binomial
- mean and variance
- MGF
- moments
- PGF
- truncated
- Poisson regression
- Polya distribution
- Pooled sample variance
- Population
- Population distribution
- Posterior probability
- Principle of,
- equivariance
- inclusion-exclusion
- invariance
- least squares
- Probability
- addition rule
- axioms
- conditional
- continuity of
- countable additivity of
- density function
- distribution
- equally likely assignment
- on finite sample spaces
- generating function
- geometric
- integral transformation
- mass function
- measure
- monotone
- multiplication rule
- posterior and prior
- principle of inclusion-exclusion
- space
- subadditivity
- tail
- total
- uniform assignment of
- Probability integral transformation
- Probit regression
- Problem,
- of location
- of location and symmetry
- of moments
- P-value
- Quadratic form
- Quantile of order p = (100p)th percentile
- Random
- Random experiment = statistical experiment
- Random interval
- coverage of
- Random sample
- from a finite population
- from a probability distribution
- Random sampling
- Random set, family of
- Random variable(s)
- bivariate
- continuous type
- discrete type
- degenerate
- equivalent
- exchangeable
- functions of a
- multiple = multivariate
- standardized
- symmetric
- symmetrized
- truncated
- uncorrelated
- Range
- Rank correlation coefficient
- Rayleigh distribution
- Realization of a sample
- Rectangular distribution
- Regression
- coefficient
- linear
- logistic
- model
- multiple
- Poisson
- probit
- Regularity conditions of FCR inequality
- Resampling
- Risk function
- Robust estimator(s)
- Robust test(s)
- Robustness, of chi-square test
- of sample mean as an estimator
- of sample standard deviation as an estimator
- of Student’s f-test
- Robust procedure, defined
- Rules of counting
- Run
- Run test
- Sample
- correlation coefficient
- covariance
- DF
- mean
- median
- distribution of
- MGF
- moments
- ordered
- point
- quantile of order p
- random
- regression coefficient
- space
- statistic(s)
- standard deviation
- standard error
- variance
- Sampling with and without replacement
- Sampling from bivariate normal
- distribution of sample correlation
- coefficient
- distribution of sample regression coefficient
- independence of sample mean vector and dispersion matrix
- Sampling from univariate normal
- distribution of sample variance
- independence of
and S2
- Scale family
- Sequence of events
- limit inferior
- limit set
- limit superior
- nondecreasing
- nonincreas ng
- Set function
- Shortest-length confidence interval(s)
- for the mean of normal
- for the parameter of exponential
- for the parameter of uniform
- for the variance of normal
- σ-field
- choice of
- generated by a class = smallest
- Sign test
- Similar tests
- Single-sample problem(s)
- of fit
- of location
- and symmetry
- Skewness, coefficient of
- Slow variation, function of
- Slutsky’s theorem
- Spearman’s rank correlation coefficient
- distribution
- Stable distribution
- Standard deviation
- Standard error
- Standardized RV
- Statistic of order k
- marginal PDF
- Stirling’s approximation
- Stochastically larger
- Strong law of large numbers
- Borel’s
- Kolmogorov’s
- Student’s t-distribution, central
- bivariate
- moments
- noncentral
- moments
- Student’s t- statistic
- Student’s t- test
- as generalized likelihood ratio test
- for paired observations
- robustness of
- Substitution principle
- estimator
- Sufficient statistic
- factorization criterion
- joint
- Sufficient statistic for, Bernoulli
- beta
- discrete uniform
- gamma
- lognormal
- normal
- Poisson
- uniform
- Support, of a DF
- Survival function = reliability function
- Symmetric DF or RV
- Symmetrization
- Symmetrized rv
- Symmetry, center of
- Tail probabilities
- Test(s),
- α-similar
- chi-square
- critical = rejection region
- critical function
- of hypothesis
- F-
- invariant
- level of significance
- locally most powerful
- most powerful
- nonrandomized
- one-tailed
- power function
- randomized
- similar
- size
- statistic
- Student’s t
- two tailed
- unbiased
- uniformly most powerful
- Testing the hypothesis of, equality of several normal means
- goodness-of- fit
- homogeneity
- independence
- Tests of hypothesis, Bayes
- GLR
- minimax
- Neyman-Pears
- Tests of location
- sign test
- Wilcoxon signed-rank
- Tolerance coefficient and interval
- Total probability rule
- Transformation
- of continuous type
- of discrete type
- Helmert
- Jacobian of
- not one-to-one
- one-to-one
- Triangular distribution
- Trimmed mean
- Trinomial distribution
- Truncated distribution
- Truncated RVs
- Truncation
- Two-point distribution
- Two-sample problems
- Types of error in testing hypotheses
- Unbiased confidence interval(s)
- general method of construction
- for mean of normal
- for parameter of exponential
- for parameter of uniform
- for variance of normal
- Unbiased estimator
- best linear
- and complete sufficient statistic
- LMV
- and sufficient statistic
- UMV
- Unbiased estimation for parameter of,
- Bernoulli
- bivariate normal
- discrete uniform
- exponential
- hypergeometric
- negative binomial
- normal
- Poisson
- Unbiased test
- for mean of normal
- and similar test
- UMP
- Uncorrelated RVs
- Uniform distribution
- characterization
- discrete
- generating samples
- MGF
- moments
- statistic of order k
- truncated
- UMP test(s)
- α-similar
- invariant
- unbiased
- U-statistic
- for estimating mean and variance
- one-sample
- two-sample
- Variance
- properties of
- of sum of RVs
- Variance stablizing transformations
- Weak law of large numbers
- centering and norming constants
- Weibull distribution
- Welch approximate t-test
- Wilcoxon signed-rank test
- Wilcoxon statistic
- distribution
- generating function
- moments
- Winsorization
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