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Mathematical theory of statistics, concerned with formal definitions and general results.
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explanation of proof that sample mean is unbiased
William Cochran's book on sampling gives the following proof that a sample mean is unbiased:
Since every unit appears in the same number of samples, it is clear that $E[Y_1 + \cdots + Y_n]$ must be …
3
votes
When do we use local alternatives?
The LAN use mentioned by @nth is in my experience a little less common in practice, and mainly of theoretical interest. More common uses I know of are
Relative efficiency of estimators: since most re …