# 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 in the central limit theorem for the number of maxima of random samples chosen uniformly at random from the right triangle of the shape

. 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.