On the (im-)possibility of representing probability distributions as a difference of i.i.d. noise terms

Arbeitspapier

A random variable is difference-form decomposable (DFD) if it may be written as the difference of two i.i.d. random terms. We show that densities of such variables exhibit a remarkable degree of structure. Specifically, a DFD density can be neither approximately uniform, nor quasiconvex, nor strictly concave. On the other hand, a DFD density need, in general, be neither unimodal nor logconcave. Regarding smoothness, we show that a compactly supported DFD density cannot be analytic and will often exhibit a kink even if its components are smooth. The analysis highlights the risks for model consistency resulting from the strategy widely adopted in the economics literature of imposing assumptions directly on a difference of noise terms rather than on its components.

Angaben zum Objekt

• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: Series: Working Paper ; No. 428

Klassifikation und Themen

• Klassifikation: Wirtschaft ; Specific Distributions; Specific Statistics
• Thema: Differences of random variables ; density functions ; characteristic function ; uniform distribution

Beteiligte, Orts- und Zeitangaben

• Ereignis: Geistige Schöpfung
• (wer): Ewerhart, Christian ; Serena, Marco
• Ereignis: Veröffentlichung
• (wer): University of Zurich, Department of Economics
• (wo): Zurich
• (wann): 2023

Weitere Informationen

• DOI: doi:10.5167/uzh-231569
• Handle: http://hdl.handle.net/10419/270435
• Letzte Aktualisierung: 10.03.2025, 11:46 MEZ