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In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. It has given rise to many popular estimators such as the Wiener–Kolmogorov filter and Ka

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rdf:type	software
rdfs:label	Minimum mean square error (en) 最小均方误差 (zh)
rdfs:comment	在統計學和信号处理中，最小均方误差（英語：Minimum mean-square error，缩写MMSE）估計是一种使均方误差（MSE）最小化的估计函数，其通常被称为最优估计。 (zh) In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. It has given rise to many popular estimators such as the Wiener–Kolmogorov filter and Ka (en)
dcterms:subject	Statistical deviation and dispersion Point estimation performance Signal estimation
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Wikipage revision ID	1106846911 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar (mathematics) Statistical deviation and dispersion Point estimation performance Uniform distribution (continuous) Levinson recursion Zero-forcing equalizer Conjugate gradient method Estimator Gauss–Markov theorem Monte Carlo methods Orthogonality principle Cholesky decomposition Signal processing Statistics Adaptive filter Trace (linear algebra) Least mean squares filter Least squares Linear prediction Minimum-variance unbiased estimator Signal estimation Expected value Bayes theorem Kalman filter Dependent variable Stochastic gradient descent QR decomposition Recursive least squares filter Covariance matrix Efficiency (statistics) Toeplitz matrix Wiener filter Mean square error Loss function Mean squared error Wide sense stationary Fisher information Asymptotically unbiased Bayesian estimator Gauss elimination Jointly Gaussian Pearson's correlation coefficient
Link from a Wikipage to an external page	http://cnx.rice.edu/content/m11267/latest/ https://archive.org/details/fundamentalsstat00kays_032 https://archive.org/details/fundamentalsstat00kays_032/page/n352 https://archive.org/details/predictionimprov0000bibb https://web.archive.org/web/20080725052939/http:/cnx.rice.edu/content/m11267/latest/
sameAs	Minimum mean square error Minimum mean square error Minimum mean square error Minimum mean square error
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has abstract	In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. It has given rise to many popular estimators such as the Wiener–Kolmogorov filter and Kalman filter. (en) 在統計學和信号处理中，最小均方误差（英語：Minimum mean-square error，缩写MMSE）估計是一种使均方误差（MSE）最小化的估计函数，其通常被称为最优估计。 (zh)
gold:hypernym	Method
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is Link from a Wikipage to another Wikipage of	Minimax estimator Best linear unbiased prediction Point estimation Multi-user MIMO Equalization (communications) Orthogonality principle Polarization-division multiplexing Probabilistic data association filter Joint Probabilistic Data Association Filter Least squares Linear least squares Linear prediction Minimum-variance unbiased estimator Kalman filter Principal component analysis Wiener filter Ordinary least squares MMSE Mean squared error List of statistics articles Statistic Smart antenna Minimum mean-square error Minimum mean-square error estimate

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