RT Journal Article
SR 00
ID 10.1111/rssb.12098
A1 Daouia, Abdelaati
A1 Noh, Hohsuk
A1 Park, Byeong U.
T1 Data envelope fitting with constrained polynomial splines
JF Journal of the Royal Statistical Society: Series B (Statistical Methodology)
YR 2016
FD 2016
VO 78
IS 1
SP 3
OP 30
K1 Boundary curve
K1 Concavity
K1 Least majorant
K1 Linear programming
K1 Monotone smoothing
K1 Multiple shape constraints
K1 Polynomial spline
K1 Second-order cone programming
AB Estimation of support frontiers and boundaries often involves monotone and/or concave edge data smoothing. This estimation problem arises in various unrelated contexts, such as optimal cost and production assessments in econometrics and master curve prediction in the reliability programmes of nuclear reactors. Very few constrained estimators of the support boundary of a bivariate distribution have been introduced in the literature. They are based on simple envelopment techniques which often suffer from lack of precision and smoothness. Combining the edge estimation idea of Hall, Park and Stern with the quadratic spline smoothing method of He and Shi, we develop a novel constrained fit of the boundary curve which benefits from the smoothness of spline approximation and the computational efficiency of linear programmes. Using cubic splines is also feasible and more attractive under multiple shape constraints; computing the optimal spline smoother is then formulated as a second-order cone programming problem. Both constrained quadratic and cubic spline frontiers have a similar level of computational complexity to those of the unconstrained fits and inherit their asymptotic properties. The utility of this method is illustrated through applications to some real data sets and simulation evidence is also presented to show its superiority over the best-known methods.
PB Wiley
SN 1369-7412
LK https://publications.ut-capitole.fr/id/eprint/16903/
UL http://tse-fr.eu/pub/29302