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Therefore, a naïve algorithm to calculate the estimated variance is given by the following: Let n ← 0, Sum ← 0, SumSq ← 0. For each datum x : n ← n + 1. Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply ...
Definition and basic properties. 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).
Triangular. In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b, and mode c, where a < b and a ≤ c ≤ b .
The variance of a random variable is the expected value of the squared deviation from the mean of , : This definition encompasses random variables that are generated by processes that are discrete, continuous, neither, or mixed. The variance can also be thought of as the covariance of a random variable with itself:
Maximum likelihood estimation. In statistics, maximum likelihood estimation ( MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
Inverse-variance weighting. In statistics, inverse-variance weighting is a method of aggregating two or more random variables to minimize the variance of the weighted average. Each random variable is weighted in inverse proportion to its variance (i.e., proportional to its precision ). Given a sequence of independent observations yi with ...
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them.
Applied to one vector, the covariance matrix maps a linear combination c of the random variables X onto a vector of covariances with those variables: . Treated as a bilinear form, it yields the covariance between the two linear combinations: . The variance of a linear combination is then , its covariance with itself.