Comparing weak and strong convergence of density functions

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Comparing weak and strong convergence of density functions

Walker, Stephen G.

Statistics & probability letters, September 2023, 2023-09-00, Volume: 200

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Weak convergence of a distribution does not imply the density converges with respect to the L1 metric. We prove that strong convergence can be established by showing that a smoothed and non-smoothed sequence of the densities converge to each other.

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