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Why is/was "consistency" of estimators desired?
In an article, I found while researching another thread ("Revisiting a 90-year-old debate: the advantages of the mean deviation", http://www.leeds.ac.uk/educol/documents/00003759.htm ), the author states this bit of statistics history:
I recognize the description of "sufficient" and "efficient" as modern criteria. But the description of "consistent" seems rather simple minded. Was the idea of "consistent" that if the estimator and the population parameter were calculated "in the same way" that the probability of the estimate being near true value of the parameter would approach 1.0 as the sample size approached infinity?
In an article, I found while researching another thread ("Revisiting a 90-year-old debate: the advantages of the mean deviation", http://www.leeds.ac.uk/educol/documents/00003759.htm ), the author states this bit of statistics history:
Fisher had proposed that the quality of any statistic could be judged in terms of three characteristics. The statistic, and the population parameter that it represents, should be consistent (i.e. calculated in the same way for both sample and population). The statistic should be sufficient in the sense of summarising all of the relevant information to be gleaned from the sample about the population parameter. In addition, the statistic should be efficient in the sense of having the smallest probable error as an estimate of the population parameter. Both SD and MD meet the first two criteria (to the same extent). According to Fisher, it was in meeting the last criteria that SD proves superior.
I recognize the description of "sufficient" and "efficient" as modern criteria. But the description of "consistent" seems rather simple minded. Was the idea of "consistent" that if the estimator and the population parameter were calculated "in the same way" that the probability of the estimate being near true value of the parameter would approach 1.0 as the sample size approached infinity?