... smoothest1
A smooth curve here is one with no rapid changes or oscillations, so the smoothest is the one with the least change in slope over its length.
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... linear2
Write a linear segment as , so summing several linear segments, at the point gives which is obviously a linear segment.
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... averaged3
A shifted histogram being one with the same data and bin width but with a different starting point on the x axis.
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... function4
A probability density function is a function f defined on an interval (a, b) and having the following properties.

1. for every
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... estimator5
For nearest neighbour the density is taken to be inversely proportional to the distance between the data item and the next nearest, by some measure, data item.
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... sphere6
The volume of the dimensional sphere is given by
 (20)

see McDonald (2003) for derivation and evaluations of . This gives values for as follows

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