Editing Estimation theory (section)

{{Short description|Branch of statistics to estimate models based on measured data}}
{{redirect-distinguish|Parameter estimation|Point estimation|Interval estimation}}
{{other uses|Estimation (disambiguation)}}
{{More footnotes|date=April 2025}}
'''Estimation theory''' is a branch of [[statistics]] that deals with estimating the values of [[Statistical parameter|parameters]] based on measured empirical data that has a random component.  The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An ''[[estimator]]'' attempts to approximate the unknown parameters using the measurements.
In estimation theory, two approaches are generally considered:<ref>
{{cite book |last1=Walter |first1=E. |last2=Pronzato |first2=L. |title=Identification of Parametric Models from Experimental Data |year=1997 |publisher=Springer-Verlag |location=London, England }}
</ref>

* The probabilistic approach (described in this article) assumes that the measured data is random with [[probability distribution]] dependent on the parameters of interest
* The [[set estimation|set-membership approach]] assumes that the measured data vector belongs to a set which depends on the parameter vector.