Total variation convergence preserves conditional independence

Forskning

Total variation convergence preserves conditional independence

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Total variation convergence preserves conditional independence. / Lauritzen, Steffen.

In: Statistics and Probability Letters, Vol. 214, 110200, 2024.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Lauritzen, S 2024, 'Total variation convergence preserves conditional independence', Statistics and Probability Letters, vol. 214, 110200. https://doi.org/10.1016/j.spl.2024.110200

APA

Lauritzen, S. (2024). Total variation convergence preserves conditional independence. Statistics and Probability Letters, 214, [110200]. https://doi.org/10.1016/j.spl.2024.110200

Vancouver

Lauritzen S. Total variation convergence preserves conditional independence. Statistics and Probability Letters. 2024;214. 110200. https://doi.org/10.1016/j.spl.2024.110200

Author

Lauritzen, Steffen. / Total variation convergence preserves conditional independence. In: Statistics and Probability Letters. 2024 ; Vol. 214.

Bibtex

@article{5aeb2b5fd6564893ab251df75fe052f4,

title = "Total variation convergence preserves conditional independence",

abstract = "This note establishes that if a sequence Pn,n=1,… of probability measures converges in total variation to the limiting probability measure P, and σ-algebras A and B are conditionally independent given H with respect to Pn for all n, then they are also conditionally independent with respect to the limiting measure P. As a corollary, this also extends to pointwise convergence of densities to a density.",

keywords = "Markov properties, Scheff{\'e}{\textquoteright}s theorem",

author = "Steffen Lauritzen",

note = "Publisher Copyright: {\textcopyright} 2024 The Author(s)",

year = "2024",

doi = "10.1016/j.spl.2024.110200",

language = "English",

volume = "214",

journal = "Statistics & Probability Letters",

issn = "0167-7152",

publisher = "Elsevier BV * North-Holland",

}

RIS

TY - JOUR

T1 - Total variation convergence preserves conditional independence

AU - Lauritzen, Steffen

PY - 2024

Y1 - 2024

N2 - This note establishes that if a sequence Pn,n=1,… of probability measures converges in total variation to the limiting probability measure P, and σ-algebras A and B are conditionally independent given H with respect to Pn for all n, then they are also conditionally independent with respect to the limiting measure P. As a corollary, this also extends to pointwise convergence of densities to a density.

AB - This note establishes that if a sequence Pn,n=1,… of probability measures converges in total variation to the limiting probability measure P, and σ-algebras A and B are conditionally independent given H with respect to Pn for all n, then they are also conditionally independent with respect to the limiting measure P. As a corollary, this also extends to pointwise convergence of densities to a density.

KW - Markov properties

KW - Scheffé’s theorem

UR - http://www.scopus.com/inward/record.url?scp=85197129167&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2024.110200

DO - 10.1016/j.spl.2024.110200

M3 - Journal article

AN - SCOPUS:85197129167

VL - 214

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

SN - 0167-7152

M1 - 110200

ER -

ID: 397609715