Donsker's Theorem for Discretized Data

Donsker's Theorem for Discretized Data

In the Kolmogorov-Smirnov theorem, the underlying distribution is assumed to be a continuous distribution. On the other hand, real data in practice is always given in a discretized (rounded) form. In this paper we establish a Donsker type theorem in the fashion of the modern empirical process theory...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:JOURNAL OF THE JAPAN STATISTICAL SOCIETY 2009/02/24, Vol.38(3), pp.505-515
1. Verfasser: Nishiyama, Yoichi
Format: Artikel
Sprache:eng
Schlagworte:
Discretized observation
empirical process
goodness of fit test
invariance principle
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In the Kolmogorov-Smirnov theorem, the underlying distribution is assumed to be a continuous distribution. On the other hand, real data in practice is always given in a discretized (rounded) form. In this paper we establish a Donsker type theorem in the fashion of the modern empirical process theory to obtain a (right) Kolmogorov-Smirnov test for discretized data.
ISSN:1882-2754
1348-6365
DOI:10.14490/jjss.38.505