Limit Theory in Monotone Function Estimation

• Autores: Cécile Durot, Hendrik P. Lopuhaä
• Localización: Statistical science, ISSN 0883-4237, Vol. 33, Nº. Extra 4, 2018 (Ejemplar dedicado a: Nonparametric Inference Under Shape Constraints), págs. 547-567
• Idioma: inglés
• DOI: 10.1214/18-sts664
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• Resumen

  • We give an overview of the different concepts and methods that are commonly used when studying the asymptotic properties of isotonic estimators.

    After introducing the inverse process, we illustrate its use in establishing weak convergence of the estimators at a fixed point and also weak convergence of global distances, such as the Lp-distance and supremum distance.

    Furthermore, we discuss the developments on smooth isotonic estimation.