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The term MMSE more specifically refers to estimation in a Bayesian setting with quadratic cost function. The basic idea behind the Bayesian approach to estimation stems from practical situations where we often have some prior information about the parameter to be estimated.
The MSE either assesses the quality of a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable), or of an estimator (i.e., a mathematical function mapping a sample of data to an estimate of a parameter of the population from which the data is sampled).
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Let (+) be an unknown signal which must be estimated from a measurement signal (), where is a tunable parameter. > is known as prediction, = is known as filtering, and < is known as smoothing (see Wiener filtering chapter of [1] for more details).
In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.
MMSE can refer to: Mini–mental state examination, a questionnaire to measure cognitive impairment; Minimum mean square error, an estimation method that minimizes the mean square error; Multimedia Messaging Service Environment, the servers in a mobile telephony network required for Multimedia Messaging Service messaging.
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.
MMSE is basically a Bayesian concept, since from a frequentist point of view there is no single minimum MSE estimator. This should be made clear right from the top ...