Total variation convergence preserves conditional independence
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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.
Original language | English |
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Article number | 110200 |
Journal | Statistics and Probability Letters |
Volume | 214 |
ISSN | 0167-7152 |
DOIs | |
Publication status | Published - 2024 |
Bibliographical note
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© 2024 The Author(s)
- Markov properties, Scheffé’s theorem
Research areas
ID: 397609715