On polynomial estimators of frontiers and boundaries

Peter Hall, Byeong U. Park, Steven E. Stern

Research output: Contribution to journalArticleResearchpeer-review

40 Citations (Scopus)

Abstract

Motivated by problems of frontier estimation in productivity analysis, and boundary estimation in scatter-point image analysis, we consider polynomial-based estimators of the edge of a distribution. Our aim is to develop methods for correcting polynomial-type estimators of bias, and for constructing simultaneous confidence bands for the data edge. We tackle this problem by first deriving large-sample approximations to distributions of polynomial-based edge estimators, and then developing algorithms for simulating from them so as to produce Monte Carlo approximations to the distribution of the difference between the true edge and its estimator. This involves applying representations for joint extreme value distributions. The majority of attention is focused on the parametric case, but nonparametric problems, where polynomial approximations are fitted locally, are also considered.

Original languageEnglish
Pages (from-to)71-98
Number of pages28
JournalJournal of Multivariate Analysis
Volume66
Issue number1
DOIs
Publication statusPublished - Jul 1998
Externally publishedYes

Fingerprint

Polynomials
Estimator
Polynomial
Polynomial approximation
Simultaneous Confidence Bands
Extreme Value Distribution
Image analysis
Polynomial Approximation
Approximation
Scatter
Productivity
Image Analysis
Confidence
Frontier estimation
Productivity analysis
Extreme values

Cite this

Hall, Peter ; Park, Byeong U. ; Stern, Steven E. / On polynomial estimators of frontiers and boundaries. In: Journal of Multivariate Analysis. 1998 ; Vol. 66, No. 1. pp. 71-98.
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On polynomial estimators of frontiers and boundaries. / Hall, Peter; Park, Byeong U.; Stern, Steven E.

In: Journal of Multivariate Analysis, Vol. 66, No. 1, 07.1998, p. 71-98.

Research output: Contribution to journalArticleResearchpeer-review

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