Suppose that a sequence $F_{n}$ of distribution functions converge pointwise to a distribution function.
So my question if does the sequence of the quantile functions (associated to $F_{n}$) converge pointwise ?
Thanks and regards.
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Yes, convergence of the two functions at continuity points of the limit is in fact equivalent. – Galton Nov 11 '19 at 16:06
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Okay thank you, this result solve my question do you have a proof ? – Nov 11 '19 at 18:53
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I do but I believe there is an expectation here for you to make some attempt at solving it yourself. If you don't want to go that route, refer to chapter 21 of van der Vaart's Asymptotic Statistics. – Galton Nov 11 '19 at 19:49
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Does this answer your question? convergence in distribution and convergence of quantile – user159517 Jun 04 '24 at 07:42