Length and surface area estimation under smoothness restrictions
2008 ◽
Vol 40
(02)
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pp. 348-358
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Keyword(s):
The problem of estimating the Minkowski content L 0(G) of a body G ⊂ ℝ d is considered. For d = 2, the Minkowski content represents the boundary length of G. It is assumed that a ball of radius r can roll inside and outside the boundary of G. We use this shape restriction to propose a new estimator for L 0(G). This estimator is based on the information provided by a random sample, taken on a square containing G, in which we know whether a sample point is in G or not. We obtain the almost sure convergence rate for the proposed estimator.
2008 ◽
Vol 40
(2)
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pp. 348-358
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Keyword(s):
Keyword(s):
1993 ◽
Vol 80
(2-3)
◽
pp. 257-260
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2018 ◽
Vol 342
◽
pp. 25-36
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2020 ◽
Vol 65
(3)
◽
pp. 1295-1302
2007 ◽
Vol 28
(1)
◽
pp. 42-48
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Keyword(s):
2011 ◽
Vol 196
(17)
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pp. 7076-7089
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Keyword(s):