 ... smoothest^{1}
 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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 ...
linear^{2}
 Write a linear segment as
, so summing several
linear segments, at the point gives
which is obviously a linear
segment.
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 ... averaged^{3}
 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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 ... function^{4}
 A probability
density function is a function f defined on an interval (a, b) and having the
following properties.
 for every

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 ... estimator^{5}
 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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 ...
sphere^{6}
 The volume of the dimensional sphere is given by
see McDonald (2003) for derivation and evaluations of .
This gives values for as follows
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