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Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available. [ 1 ]
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. [1] For example, the sample mean is a commonly used estimator of the population mean. There are point and interval ...
A function of the known data that is used to estimate an unknown parameter; an estimate is the result of the actual application of the function to a particular set of data. For example, the mean can be used as an estimator. expected value. Also expectation, mathematical expectation, first moment, or simply mean or average.
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].
The basis of the method is to have, or to find, a set of simultaneous equations involving both the sample data and the unknown model parameters which are to be solved in order to define the estimates of the parameters. [1] Various components of the equations are defined in terms of the set of observed data on which the estimates are to be based.
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.
Approximation theory is a branch of mathematics, and a quantitative part of functional analysis. Diophantine approximation deals with approximations of real numbers by rational numbers . Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain.
Depending on authors, the term "maps" or the term "functions" may be reserved for specific kinds of functions or morphisms (e.g., function as an analytic term and map as a general term). mathematics See mathematics. multivalued A "multivalued function” from a set A to a set B is a function from A to the subsets of B.