<P> In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors or deviations--that is, the difference between the estimator and what is estimated . MSE is a risk function, corresponding to the expected value of the squared error loss or quadratic loss . The difference occurs because of randomness or because the estimator doesn't account for information that could produce a more accurate estimate . </P> <P> The MSE is a measure of the quality of an estimator--it is always non-negative, and values closer to zero are better . </P> <P> The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator and its bias . For an unbiased estimator, the MSE is the variance of the estimator . Like the variance, MSE has the same units of measurement as the square of the quantity being estimated . In an analogy to standard deviation, taking the square root of MSE yields the root - mean - square error or root - mean - square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard deviation . </P> <P> The MSE assesses the quality of an estimator (i.e., a mathematical function mapping a sample of data to a parameter of the population from which the data is sampled) or a predictor (i.e., a function mapping arbitrary inputs to a sample of values of some random variable). Definition of an MSE differs according to whether one is describing an estimator or a predictor . </P>

Is root mean square error the same as standard deviation