MINIMUM MEAN SQUARE ERROR Meaning and
Definition
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Minimum mean square error (MMSE) is a statistical term that refers to the method of estimating an unknown quantity by minimizing the mean square error between the estimated value and the actual value. It is commonly used in the field of signal processing and statistics to create efficient estimators.
In practical terms, MMSE is a technique to reduce the discrepancy between predicted values and real values by finding the optimal estimation. It calculates the expected value of the squared difference between the predicted and actual values, aiming to achieve the smallest average error.
The MMSE is derived from the concept of finding the conditional expectation and employing the law of iterated expectations. It is a common approach used when the values being estimated are subject to random variations or noise. By minimizing the mean square error, MMSE forms an estimation technique that is optimal under certain conditions, particularly when the values are normally distributed or when the estimation task falls within the framework of linear regression.
Furthermore, the MMSE estimator can be applied in various areas such as telecommunications, image processing, and machine learning, where accurate estimation of unknown quantities is essential. The MMSE method has proven to be a powerful tool in modeling and prediction by providing a systematic way to reduce errors and improve the accuracy of estimations.
