RT Journal Article
T1 Polynomial volume estimation and its applications
A1 Cuevas González, Antonio
A1 Pateiro López, Beatriz
K1 Set estimation
K1 Volume estimation
K1 Boundary length estimation
AB Given a compact set S ⊂ Rd we consider the problem of estimating, from a random sample of points, the Lebesgue measure of S, µ(S), and its boundary measure, L(S) (as definedby the Minkowski content of ∂S). This topic has received some attention, especially in thetwo-dimensional case d = 2, motivated by applications in image analysis. A new method tosimultaneously estimate µ(S) and L(S) from a sample of points inside S is proposed.The basic idea is to assume that S has a polynomial volume, that is, that V (r) := µ{x :d(x, S) ≤ r} is a polynomial in r of degree d, for all r in some interval [0, R). We develop aminimum distance approach to estimate the coefficients of V (r) and, in particular µ(S) and L(S),which correspond, respectively, to the independent term and the first degree coefficient of V (r).The strong consistency of the proposed estimators is proved. Some numerical illustrations aregiven
PB Elsevier
SN 0378-3758
YR 2018
FD 2018
LK http://hdl.handle.net/10347/18631
UL http://hdl.handle.net/10347/18631
LA eng
NO Antonio Cuevas, Beatriz Pateiro-López (2018) Polynomial volume estimation and its applications, Journal of Statistical Planning and Inference, Volume 196, pp 174-184, DOI: 10.1016/j.jspi.2017.11.005
NO This work has been partially supported by Spanish Grants MTM2016-78751-P (A. Cuevas) and MTM2016-76969-P (B. Pateiro-López)
DS Minerva
RD 4 may 2026