Mathematical Statistics

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Mathematical Statistics

Statistical Inference

hypothesis test

parameter estimation

interval

point

Point Estimator

UMVUE

充分完备统计量

CR inequation

iid

conclusion

UE and another condition

smooth condition

Fisher 信息量

regular condition

一致最优估计

Assessment

bias

biased

unbiased | UE

estimable

MSEM

相对效率 = MSEM / MSEM

MESM = Var + bias^2

MESM = Var

Method

maximum likelyhood estimator | MLE

moment estimator

Basic

Distributions

continuous

multivariate normal

gamma

Z

beta

cauchy

normal

F

t

x2

exponential

uniform

discrete

multinomial

0-1-...-k

poisson

binomial

0-1

Statistics

sufficient statistic

# ordered is sufficient

general

4

empirical distribution function

3

sample kurtosis

sample skewness

sample coefficient of variation

2

sample p-fractile / p-quantile

extreme of sample

sample median

ordered statistics

1

sample covariance / relavant

sample moment

sample variation / sd

sample mean

sampling distribution

Sample

sampling

simple random sample

i.i.d.

r.v. | observation

sample size

sample space

Population

distribution

distribution family

exponential family

r.v.