Examples and Problems in Mathematical Statistics

List of Abbreviations

a.s.	Almost surely
ANOVA	Analysis of variance
c.d.f.	Cumulative distribution function
cov(x,y)	Covariance of X and Y
CI	Confidence interval
CLT	Central limit theorem
CP	Coverage probability
CR	Cramer Rao regularity conditions
E {X| Y}	Conditional expected value of X, given Y
E {X}	Expected value of X
FIM	Fisher information matrix
i.i.d.	Independent identically distributed
LBUE	Linear best unbiased estimate
LCL	Lower confidence limit
m.g.f.	Moment generating function
m.s.s.	Minimal sufficient statistics
MEE	Moments equations estimator
MLE	Maximum likelihood estimator
MLR	Monotone likelihood ratio
MP	Most powerful
MSE	Mean squared error
MVU	Minimum variance unbiased
OC	Operating characteristic
p.d.f.	Probability density function
p.g.f.	Probability generating function
P {E| A}	Conditional probability of E, given A
P {E}	Probability of E
PTE	Pre–test estimator
r.v.	Random variable
RHS	Right–hand side
s.v.	Stopping variable
SE	Standard error
SLLN	Strong law of large numbers
SPRT	Sequential probability ratio test
tr {A}	trace of the matrix A
UCL	Upper control limit
UMP	Uniformly most powerful
UMPI	Uniformly most powerful invariant
UMPU	Uniformly most powerful unbiased
UMVU	Uniformly minimum variance unbiased
V {X| Y}	Conditional variance of X, given Y
V {X}	Variance of X
w.r.t.	With respect to
WLLN	Weak law of large numbers