A Statistical Proof of the Transformation Theorem

Posted: 19 Mar 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

J.R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics

Date Written: March 17, 2012

Abstract

The well-known transformation theorem (or change-of-variables theorem) is difficult to prove, requiring knowledge of theorems in advanced analysis. For this reason, it is stated without proof in all the statistics textbooks we know of. Here, we provide a new and much simpler proof, by exploiting the fact that it is a density function which is being transformed, and the idea of conditioning.

Suggested Citation

Abadir, Karim M. and Magnus, Jan R., A Statistical Proof of the Transformation Theorem (March 17, 2012). Available at SSRN: https://ssrn.com/abstract=2025472

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Jan R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

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