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In statistics, a circumflex (ˆ), called a "hat", is used to denote an estimator or an estimated value. [1] For example, in the context of errors and residuals , the "hat" over the letter ε ^ {\displaystyle {\hat {\varepsilon }}} indicates an observable estimate (the residuals) of an unobservable quantity called ε {\displaystyle \varepsilon ...
The actual values are only computed when needed. For example, one could create a function that creates an infinite list (often called a stream) of Fibonacci numbers. The calculation of the n-th Fibonacci number would be merely the extraction of that element from the infinite list, forcing the evaluation of only the first n members of the list.
As an important special case, an easy to use recursive expression can be derived when at each k-th time instant the underlying linear observation process yields a scalar such that = +, where is n-by-1 known column vector whose values can change with time, is n-by-1 random column vector to be estimated, and is scalar noise term with variance .
"Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators. Estimation theory is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same ...
Least absolute deviations (LAD), also known as least absolute errors (LAE), least absolute residuals (LAR), or least absolute values (LAV), is a statistical optimality criterion and a statistical optimization technique based on minimizing the sum of absolute deviations (also sum of absolute residuals or sum of absolute errors) or the L 1 norm of such values.
The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). [citation needed] For an unbiased estimator, the MSE is the variance of the ...
If the maximum number of leading zeros observed is n, an estimate for the number of distinct elements in the set is 2 n. [1] In the HyperLogLog algorithm, a hash function is applied to each element in the original multiset to obtain a multiset of uniformly distributed random numbers with the same cardinality as the original multiset. The ...
[1] [2] In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate; that is, estimate the value of that function for an intermediate value of the independent ...