Methods for tracking support boundaries with corners
AbstractIn a range of practical problems the boundary of the support of a bivariate distribution is of interest, for example where it describes a limit to efficiency or performance, or where it determines the physical extremities of a spatially distributed population in forestry, marine science, medicine, meteorology or geology. We suggest a tracking-based method for estimating a support boundary when it is composed of a finite number of smooth curves, meeting together at corners. The smooth parts of the boundary are assumed to have continuously turning tangents and bounded curvature, and the corners are not allowed to be infinitely sharp; that is, the angle between the two tangents should not equal [pi]. In other respects, however, the boundary may be quite general. In particular it need not be uniquely defined in Cartesian coordinates, its corners my be either concave or convex, and its smooth parts may be neither concave nor convex. Tracking methods are well suited to such generalities, and they also have the advantage of requiring relatively small amounts of computation. It is shown that they achieve optimal convergence rates, in the sense of uniform approximation.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 97 (2006)
Issue (Month): 8 (September)
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- Muller, H. G. & Song, K. S., 1994. "Maximin Estimation of Multidimensional Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 265-281, August.
- Park, B. U. & Sickles, R. C. & Simar, L., 1998.
"Stochastic panel frontiers: A semiparametric approach,"
Journal of Econometrics,
Elsevier, vol. 84(2), pages 273-301, June.
- PARK, Byeong U. & SICKLES, Robin C. & SIMAR, Léopold, 1996. "Stochastic Panel Frontiers : A Semiparametric Approach," CORE Discussion Papers 1996038, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- PARK, Beyong U. & SICKLES, Robin C. & SIMAR, Léopold, . "Stochastic panel frontiers: A semiparametric approach," CORE Discussion Papers RP -1330, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Hall, Peter & Park, Byeong U. & Stern, Steven E., 1998. "On Polynomial Estimators of Frontiers and Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 71-98, July.
- Kneip, Alois & Park, Byeong U. & Simar, L opold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(06), pages 783-793, December.
- Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
- Tsybakov, A.B. & Korostelev, A.P. & Simar, L., 1992. "Efficient Estimation of Monotone Boundaries," Papers 9209, Catholique de Louvain - Institut de statistique.
- Peter Hall & Liang Peng & Christian Rau, 2001. "Local likelihood tracking of fault lines and boundaries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 569-582.
- Hall, Peter & Nussbaum, Michael & Stern, Steven E., 1997. "On the Estimation of a Support Curve of Indeterminate Sharpness," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 204-232, August.
- Hardle, W. & Park, B. U. & Tsybakov, A. B., 1995. "Estimation of Non-sharp Support Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 205-218, November.
- KNEIP, Alois & SIMAR, Léopold, 1995.
"A General Framework for Frontier Estimation with Panel Data,"
CORE Discussion Papers
1995060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Kneip, A. & Simar, L., . "A general framework for frontier estimation with panel data," CORE Discussion Papers RP -1224, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- repec:wop:humbsf:1998-9 is not listed on IDEAS
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