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An estimator is a rule that tells how to calculate an estimate based on the measurements contained in a sample. For example, the sample mean x^_ is an estimator for the ...

The bias of an estimator theta^~ is defined as B(theta^~)=<theta^~>-theta. (1) It is therefore true that theta^~-theta = (theta^~-<theta^~>)+(<theta^~>-theta) (2) = ...

A topology arising from a sheaf of continuous functions. It derives a natural topology from the projection operator. Etale spaces are examples of space that are not T2.

A three-dimensional shadow of a four-dimensional Klein bottle.

The paradox "This statement is false," stated in the fourth century BC. It is a sharper version of the Epimenides paradox, "All Cretans are liars...One of their own poets has ...

A more common way to describe a Euclidean ring.

A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

The group of rotations and translations.

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...