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  2. Expected mean squares - Wikipedia

    en.wikipedia.org/wiki/Expected_mean_squares

    In statistics, expected mean squares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance (ANOVA). They can be used for ascertaining which statistic should appear in the denominator in an F-test for testing a null hypothesis that a particular effect is absent.

  3. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    Any definition of expected value may be extended to define an expected value of a multidimensional random variable, i.e. a random vector X. It is defined component by component, as E[X] i = E[X i]. Similarly, one may define the expected value of a random matrix X with components X ij by E[X] ij = E[X ij].

  4. Variance - Wikipedia

    en.wikipedia.org/wiki/Variance

    The use of the term n − 1 is called Bessel's correction, and it is also used in sample covariance and the sample standard deviation (the square root of variance). The square root is a concave function and thus introduces negative bias (by Jensen's inequality ), which depends on the distribution, and thus the corrected sample standard ...

  5. Mean squared prediction error - Wikipedia

    en.wikipedia.org/wiki/Mean_squared_prediction_error

    The MSPE can be decomposed into two terms: the squared bias (mean error) of the fitted values and the variance of the fitted values: MSPE = ME 2 + VAR , {\displaystyle \operatorname {MSPE} =\operatorname {ME} ^{2}+\operatorname {VAR} ,}

  6. Mean squared error - Wikipedia

    en.wikipedia.org/wiki/Mean_squared_error

    This definition for a known, computed quantity differs from the above definition for the computed MSE of a predictor, in that a different denominator is used. The denominator is the sample size reduced by the number of model parameters estimated from the same data, ( n − p ) for p regressors or ( n − p −1) if an intercept is used (see ...

  7. Estimator - Wikipedia

    en.wikipedia.org/wiki/Estimator

    The first term represents the mean squared error; the second term represents the square of the estimator bias; and the third term represents the variance of the sample. The quality of the estimator can be identified from the comparison between the variance, the square of the estimator bias, or the MSE.

  8. Law of the unconscious statistician - Wikipedia

    en.wikipedia.org/wiki/Law_of_the_unconscious...

    In probability theory and statistics, the law of the unconscious statistician, or LOTUS, is a theorem which expresses the expected value of a function g(X) of a random variable X in terms of g and the probability distribution of X. The form of the law depends on the type of random variable X in question.

  9. Second moment method - Wikipedia

    en.wikipedia.org/wiki/Second_moment_method

    In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments.