method of moments
E665237
The method of moments is a statistical technique for estimating distribution parameters by equating sample moments to theoretical moments.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
parameter estimation technique
ⓘ
statistical estimation method ⓘ |
| advantage |
can be applied when likelihood is intractable
ⓘ
does not require full likelihood specification ⓘ |
| appliesTo |
parametric statistical models
ⓘ
probability distributions ⓘ |
| approximateDate | late 19th century ⓘ |
| basedOn | equating sample moments to theoretical moments ⓘ |
| canEstimate |
mean parameter
ⓘ
scale parameters ⓘ shape parameters ⓘ variance parameter ⓘ |
| exampleUse |
estimating parameters of the Poisson distribution
ⓘ
estimating parameters of the binomial distribution ⓘ estimating parameters of the gamma distribution ⓘ estimating parameters of the normal distribution ⓘ |
| field |
mathematical statistics
ⓘ
statistics ⓘ |
| generalization | generalized method of moments ⓘ |
| historicalOrigin | introduced by Karl Pearson NERFINISHED ⓘ |
| limitation |
higher-order moments can be unstable in finite samples
ⓘ
moment equations may have multiple solutions ⓘ moment equations may have no real solution ⓘ |
| output | parameter estimates ⓘ |
| property |
can yield biased estimators
ⓘ
estimators are consistent under regularity conditions ⓘ may be less efficient than maximum likelihood estimates ⓘ often easier to compute than maximum likelihood estimates ⓘ solves system of equations formed by matching moments ⓘ |
| relatedTo |
generalized method of moments
ⓘ
least squares estimation ⓘ maximum likelihood estimation ⓘ |
| requires | existence of required population moments ⓘ |
| step |
compute sample moments from data
ⓘ
express theoretical moments as functions of parameters ⓘ set sample moments equal to theoretical moments ⓘ solve resulting equations for parameters ⓘ |
| typicalInput |
assumed parametric family of distributions
ⓘ
random sample ⓘ |
| usedFor | estimating distribution parameters ⓘ |
| usedIn |
actuarial science
ⓘ
applied probability ⓘ econometrics ⓘ engineering ⓘ |
| usesConcept |
moment of a random variable
ⓘ
population moments ⓘ sample moments ⓘ theoretical moments ⓘ |
Referenced by (1)
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