Tsung-Hsi Tsai: Berry-Esseen Bounds for the Number of Maxima

This is a joint work with Hsien-Kuei Hwang and Zhi-Dong Bai.

We derive the optimal convergence rate $O(n^{-1/4})$ in the central limit theorem for the number of maxima of random samples chosen uniformly at random from the right triangle of the shape
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. A local limit theorem with rate is also derived. The result is then applied to the number of maxima in general planar regions (upper-bounded by some smooth decreasing curves) for which a near-optimal convergence rate to normality is established.

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