Index
A
Akaike criterion
Aliasing
Autocorrelation
partial
Autocovariance
empirical
B
Banach space
Basis space
Bayes limit
Bernoulli
scheme
variable
Berry–Esseen inequality
Bienaymé–Tchebychev inequality
Binomial approximation
Borel algebra
Borel–Cantelli lemma
Box–Cox transformation
Brown
Brownian motion
C
Cauchy–Schwarz inequality
Chapman–Robbins inequality
Characteristic function
Complete classes
Conditional
likelihood equations
maximum likelihood method
Confidence
intervals
level
region
Consistent estimators of the spectral density
Convergence
almost sure
in distribution (or weak)
in mean
in mean square (or L2)
in probability
stochastic
Corner method
Counting
Covariance
empirical
matrix
Cramer–Rao-type inequalities
Critical region (or region of rejection)
D
Data analysis
Decision
function (d.f.)
admissible
generalized Baysian
optimal
unbiased
rules
sequential rules
space
theory
Deviations between probability distributions
Differentiation
Dispersion of a real random variable
Distribution
χ2
Bernoulli
beta
binomial
Cauchy
conditional
empirical
Fisher–Snedecor
function
Gamma
negative normal
normal (Gaussian)
of a Gaussian vector
of a process
Pareto
Poisson
Student’s
theoretical
two-dimensional normal
uniform
Dominated
Lebesgue convergence
probability space
Doob’s lemma
E
Efficiency
asymptotic relative
Einstein
Eliminating the seasonality
Empirical
analysis of the observations
moments
Error
of the first kind
of the second kind
Estimation
by explosion
Estimator
biased
efficient unbiased
Gauss-Markov
maximum-likelihood
minimax
of g(θ)
of order n
robust
strict
superefficient
unbiased
Exogenous variables
Expectation value
conditional
Exponential smoothing
F
Family of densities with monotonic likelihood ratios
Fatou’s lemma
Filtering
Finance
Finite-dimensional distributions
Fisher information
matrix
Fréchet–Darmois–Cramer–Rao inequality
H
Hilbert space
Histogram
Hoeffding’s inequality
Hypothesis
alternative
composite
null
simple
I
Independence
of real random variables
Information inequality
for prediction
Insurance policy
Integral
Lebesgue
Riemann mean-square
Integrated quadratic error
Integration
mean-square
of real random variables
on measure spaces
Intensity of a Poisson process
Interpolation
Invariance
Itô’s formula
J, K, L
Jensen’s inequality
Kernel (of a space)
Law
of large numbers
of the iterated logarithm
Likelihood
equations
Limit theorems
Linear
correlation
prediction error
predictor
Lipschitz function
Loss function
M
Margins
Martingale
Matrix of second-order moments
Maximum-likelihood method
Mean
α-truncated
empirical
moving, of order q (MA(q))
Mean-square
continuity
differentiation
Measurable
function
space
Measure
σ-finite
Dirac
Lebesgue
mean
space
Spectral
Measurement errors
Median
empirical
Method of least squares
Model
ARMAX
asymptotic
Black–Scholes
Buys Ballot
contamination
exponential
linear regression
SARIMAX
Statistical
non-parametric
parametric
Modification of a process
Moment
central, of order p
of a real random variable
of order p
N
Newton–Raphson method
Neyman–Pearson lemma
non-deterministic (randomized) method
Non-parametric
methods
regression estimation
O
Operator
backward
covariance
cross-covariance
Optimal confidence region
Order statistic
Orthogonal projection
P
Particle
Periodogram
Periods of a process
Power function of the test
Power of the test
Prediction
error
horizon
Predictor
Preferable
Preference relation
Preorder
Probability
a priori
absolutely continuous
conditional
diffuse
discrete
space
Process
ARIMA
ARIMA(p,q,d)
ARMA
ARMA(p,q)
autoregressive
first order
of order p (AR(p))
canonical
continuous-time
counting
deterministic
diffusion
discrete-time
Gaussian
geometrically strongly mixing (GSM)
increment
innovation
linear
Markov
moving-average
multidimensional
Ornstein–Uhlenbeck
point
Poisson
compound
multidimensional
non-homogeneous
progressively measurable
purely non-deterministic
regular
SARIMA(p, q, d; P, Q, D)S
stationary
stochastic
strictly stationary
weakly stationary
Wiener
Product
σ-algebra
space
Prokhorov distance
Q
Quality control
Quantiles
empirical
R
Random
function
numbers
variable
vector
Realizable linear filter
Realization
Regression
linear
Regular version of the conditional probability
Risk
a posteriori
function
quadratic
robust methods
Robustness
S
Sample
Gaussian
Seasonal effects
Seasonality
Sigma (σ) algebra (σ-field)
Sigma additivity
Simulation
Size of a test
Space
action
Spectral density
empirical
Standard deviation
State
of a process
space
Statistical predictor
Statistics
applied
asymptotic
complete
descriptive
free
mathematical
sufficient
Stochastic differential equation
Sub-σ-algebra
free
sufficient
Symmetrization of an estimator
T
Tendency
Tensor product
Test
χ2
γ
λ
bilateral
convergent with asymptotic size α
Cramer–von Mises
deterministic
homogeneity
Kolmogorov–Smirnov
likelihood ratio
locally optimal
more powerful
non-deterministic
non-parametric
rank
unbiased
undistorted
uniformly more powerful (UMP)
unilateral
Wilcoxon
Theorem
Bickel–Lehmann
central limit
Cochran’s
factorization
Fubini’s
Gauss–Markov
Glivenko–Cantelli
Glivenko-Cantelli
Karhunen–Loeve
Lehman–Scheffé
Mercer’s
Pythagoras
Rao–Blackwell
transfer
variance addition
Threshold of a test
Time
arrival
inter-arrival
set
stopping
Total variation of a function
Trajectory
Trend elimination
Truncation index
Two-dimensional Gaussian variable
V
Variable
random
Variance
empirical
Verification
W, Y
Waiting time paradox
White noise
strong
weak
Wiener
Wold decomposition
Yule-Walker equations
