Total variation convergence preserves conditional independence
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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
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TY - JOUR
T1 - Total variation convergence preserves conditional independence
AU - Lauritzen, Steffen
N1 - Publisher Copyright: © 2024 The Author(s)
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