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Statistics: Difference between revisions
→Method of Moments Estimator
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** <math>E(X) = g(\theta)</math> | ** <math>E(X) = g(\theta)</math> | ||
* Then invert to get your parameters as a function of your moments | * Then invert to get your parameters as a function of your moments | ||
** <math>\theta = g(E(X))</math> | ** <math>\theta = g^{-1}(E(X))</math> | ||
* Replace population moments with sample moments | * Replace population moments with sample moments | ||
** <math>E(X) \rightarrow \bar{x}</math> | ** <math>E(X) \rightarrow \bar{x}</math> | ||
** <math>E(X^2) \rightarrow \frac{1}{n}\sum(x_i - \bar{x})^2</math> | ** <math>E(X^2) \rightarrow \frac{1}{n}\sum(x_i - \bar{x})^2</math> | ||
** <math>\hat{\theta} = g^{-1}(\bar{x})</math> | |||
===Maximum Likelihood Estimator=== | ===Maximum Likelihood Estimator=== | ||