Editing Estimator (section)

==Background==
An "estimator" or "[[point estimate]]" is a [[statistic]] (that is, a function of the data) that is used to infer the value of an unknown [[statistical parameter|parameter]] in a [[statistical model]]. A common way of phrasing it is "the estimator is the method selected to obtain an estimate of an unknown parameter". 
The parameter being estimated is sometimes called the ''[[estimand]]''. It can be either finite-dimensional (in [[parametric model|parametric]] and [[semi-parametric model]]s), or infinite-dimensional ([[semi-parametric model|semi-parametric]] and [[non-parametric model]]s).<ref>Kosorok (2008), Section 3.1, pp 35–39.</ref> If the parameter is denoted <math> \theta </math> then the estimator is traditionally written by adding a [[circumflex]] over the symbol: <math>\widehat{\theta}</math>. Being a function of the data, the estimator is itself a [[random variable]]; a particular realization of this random variable is called the "estimate". Sometimes the words "estimator" and "estimate" are used interchangeably.

The definition places virtually no restrictions on which functions of the data can be called the "estimators". The attractiveness of different estimators can be judged by looking at their properties, such as [[unbiasedness]], [[mean square error]], [[Consistent estimator|consistency]], [[asymptotic distribution]], etc. The construction and comparison of estimators are the subjects of the [[estimation theory]]. In the context of [[decision theory]], an estimator is a type of [[decision rule]], and its performance may be evaluated through the use of [[loss function]]s.

When the word "estimator" is used without a qualifier, it usually refers to point estimation. The estimate in this case is a single point in the [[parameter space]]. There also exists another type of estimator: [[interval estimator]]s, where the estimates are subsets of the parameter space.

The problem of [[density estimation]] arises in two applications. Firstly, in estimating the [[probability density function]]s of random variables and secondly in estimating the [[Spectral density|spectral density function]] of a [[time series]]. In these problems the estimates are functions that can be thought of as point estimates in an infinite dimensional space, and there are corresponding interval estimation problems.