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Statistics: Difference between revisions
→Unbiased
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In general, you should find a complete sufficient statistic using the property of exponential families.<br> | In general, you should find a complete sufficient statistic using the property of exponential families.<br> | ||
Then make it unbiased with some factors to get the UMVUE.<br> | Then make it unbiased with some factors to get the UMVUE.<br> | ||
===Properties=== | |||
====Unbiased==== | |||
An estimator <math>\hat{\theta}</math> is unbiased for <math>\theta</math> if <math>E[\hat{\theta}] = \theta</math> | |||
* <math>X_n</math> is unbiased for <math>E[X]</math> but is not consistent | |||
====Consistent==== | |||
An estimator <math>\hat{\theta}</math> is consistent for <math>\theta</math> if it converges in probability to <math>\theta</math> | |||
* Example: <math>\frac{1}{n}\sum (X-\bar{X})^2</math> is a consistent estimator | |||
: for <math>\sigma^2</math> for <math>N(\mu, \sigma^2</math> but is not unbiased. | |||
===Efficiency=== | ===Efficiency=== | ||