Log In Sign Up

Estimation of the Global Mode of a Density: Minimaxity, Adaptation, and Computational Complexity

by   Ery Arias-Castro, et al.

We consider the estimation of the global mode of a density under some decay rate condition around the global mode. We show that the maximum of a histogram, with proper choice of bandwidth, achieves the minimax rate that we establish for the setting that we consider. This is based on knowledge of the decay rate. Addressing the situation where the decay rate is unknown, we propose a multiscale variant consisting in the recursive refinement of a histogram, which is shown to be minimax adaptive. These methods run in linear time, and we prove in an appendix that this is best possible: There is no estimation procedure that runs in sublinear time that achieves the minimax rate.


page 1

page 2

page 3

page 4


An Optimal Multistage Stochastic Gradient Method for Minimax Problems

In this paper, we study the minimax optimization problem in the smooth a...

Adaptive greedy algorithm for moderately large dimensions in kernel conditional density estimation

This paper studies the estimation of the conditional density f (x, ×) of...

Distributed Nonparametric Function Estimation: Optimal Rate of Convergence and Cost of Adaptation

Distributed minimax estimation and distributed adaptive estimation under...

Discrete minimax estimation with trees

We propose a simple recursive data-based partitioning scheme which produ...

Density Estimation with Contaminated Data: Minimax Rates and Theory of Adaptation

This paper studies density estimation under pointwise loss in the settin...

Switchback Experiments under Geometric Mixing

The switchback is an experimental design that measures treatment effects...