## Bernoulli

• Bernoulli
• Volume 14, Number 2 (2008), 580-592.

### Consistency of the $α$-trimming of a probability. Applications to central regions

#### Abstract

The sequence of $α$-trimmings of empirical probabilities is shown to converge, in the Painlevé–Kuratowski sense, on the class of probability measures endowed with the weak topology, to the $α$-trimming of the population probability. Such a result is applied to the study of the asymptotic behaviour of central regions based on the trimming of a probability.

#### Article information

Source
Bernoulli, Volume 14, Number 2 (2008), 580-592.

Dates
First available in Project Euclid: 22 April 2008

https://projecteuclid.org/euclid.bj/1208872119

Digital Object Identifier
doi:10.3150/07-BEJ109

Mathematical Reviews number (MathSciNet)
MR2544103

Zentralblatt MATH identifier
1158.60338

#### Citation

Cascos, Ignacio; López-Díaz, Miguel. Consistency of the $α$-trimming of a probability. Applications to central regions. Bernoulli 14 (2008), no. 2, 580--592. doi:10.3150/07-BEJ109. https://projecteuclid.org/euclid.bj/1208872119

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