Consistency of the simple mode of a density for spatial processes

Abstract

We are concerned with estimating the mode of a density of a spatial process by kernel method under some dependency conditions. A simple estimate of the mode based only on data is considered. The approach consists of maximizing the density kernel estimate on data. An optimal rate of uniform consistency of the density estimate will be established. Strong consistency of the simple estimate of the mode with the rate of consistency will be investigated when data are spatially dependent by some general mixing conditions.