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Estimation theory is a branch of statistics that deals with estimating the values of 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.
For many estimation problems, especially in the non-parametric estimation setting, various approximate minimax estimators have been established. The design of the approximate minimax estimator is intimately related to the geometry, such as the metric entropy number , of Θ {\displaystyle \Theta } .
In statistics, the theory of minimum norm quadratic unbiased estimation (MINQUE) [1] [2] [3] was developed by C. R. Rao. MINQUE is a theory alongside other estimation methods in estimation theory , such as the method of moments or maximum likelihood estimation .
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
The orthogonality principle is most commonly used in the setting of linear estimation. [1] In this context, let x be an unknown random vector which is to be estimated based on the observation vector y. One wishes to construct a linear estimator ^ = + for some matrix H and vector c.
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 functions. When the word "estimator" is used without a qualifier, it usually refers to point estimation.
We estimate the parameter θ using the sample mean of all observations: = = . This estimator has mean θ and variance of σ 2 / n, which is equal to the reciprocal of the Fisher information from the sample. Thus, the sample mean is a finite-sample efficient estimator for the mean of the normal distribution.
Estimation statistics, or simply estimation, is a data analysis framework that uses a combination of effect sizes, confidence intervals, precision planning, and meta-analysis to plan experiments, analyze data and interpret results. [1]