Normal approximation for partial sums: general convex costs

Jérôme Dedecker; Florence Merlevède; Emmanuel Rio

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arXiv · 2603.01909

Normal approximation for partial sums: general convex costs

Jérôme Dedecker·Florence Merlevède·Emmanuel Rio

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Abstract

We provide non-asymptotic bounds and asymptotic limits for convex transport costs between the distribution of partial sums of independent and identically distributed square integrable and centered random variables and the normal distribution with mean zero and the same variance. The proof relies on controlling the transport cost by an appropriate ideal distance, combined with an adaptation of Lindeberg's method. The numerical constants and the asymptotic constants are explicit.

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Jérôme Dedecker, Florence Merlevède, Emmanuel Rio. 2026-03-02. Normal approximation for partial sums: general convex costs. https://arxiv.org/abs/2603.01909

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