10Asymptotic Theory of M‐estimators
In order to compare the performances of different estimators, and also to obtain confidence intervals for the parameters, we need their distributions. Explicit expressions exist in some simple cases, such as sample quantiles, which include the median, but even these are in general intractable. It will be necessary to resort to approximating their distributions for large 
, the so‐called asymptotic distribution.
We shall begin with the case of a single real parameter, and we shall consider general M‐estimators of a parameter 
defined by equations of the form
For location, 
has the form 
with 
; for scale, 
with 
. If (or ) is nondecreasing then is nonincreasing ...
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