Knight, Keith Asymptotic theory for \(M\)-estimators of boundaries. (English) Zbl 1270.62052 Sperlich, Stephan (ed.) et al., The art of semiparametrics. Papers based on the presentation at the conference the art of semiparametrics, Berlin, Germany, October 18–23, 2006. Heidelberg: Physica-Verlag (ISBN 3-7908-1700-7/pbk). Contributions to Statistics, 1-21 (2006). Summary: We consider some asymptotic distribution theory for \(M\)-estimators of the parameters of a linear model whose errors are non-negative; these estimators are the solutions of constrained optimization problems and their asymptotic theory is non-standard. Under weak conditions on the distribution of the errors and on the design, we show that a large class of estimators have the same asymptotic distributions in the case of i.i.d. errors; however, this invariance does not hold under non-i.i.d. errors.For the entire collection see [Zbl 1090.62504]. Cited in 4 Documents MSC: 62F12 Asymptotic properties of parametric estimators 62F10 Point estimation Keywords:constrained optimization; epi-convergence; linear programming estimator; \(M\)-estimator; point processes PDFBibTeX XMLCite \textit{K. Knight}, in: The art of semiparametrics. Papers based on the presentation at the conference the art of semiparametrics, Berlin, Germany, October 18--23, 2006. Heidelberg: Physica-Verlag. 1--21 (2006; Zbl 1270.62052) Full Text: DOI