On sequential density estimation

Sequential nonparametric density estimation

Sequential change-point detection based on direct density-ratio estimation

Change-point detection is the problem of discovering time points at which properties of time-series data change. This covers a broad range of real-world problems and has been actively discussed in the community of statistics and data mining. In this paper, we present a novel nonparametric approach to detecting the change of probability distributions of sequence data. Our key idea is to estimate...

Mixture Density Estimation Based on Maximum Likelihoodand Sequential Test

We address the problem of estimating an unknown probability density function from a sequence of input samples. We approximate the input density with a weighted mixture of a nite number of Gaussian kernels whose parameters and weights we estimate iteratively from the input samples using the Maximum Likelihood (ML) procedure. In order to decide on the correct total number of kernels we employ sim...

On Efficiency Criteria in Density Estimation

We discuss the classical efficiency criteria in density estimation and propose some variants. The context is a general density estimation scheme that contains the cases of i.i.d. or dependent random variables, in discrete or continuous time. Unbiased estimation, optimality and asymptotic optimality are considered. An example of a density estimator that satisfies some suggested criteria is given...

Density Estimation via Discrepancy Based Adaptive Sequential Partition

Given iid observations from an unknown absolute continuous distribution defined on some domain Ω, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function. Our density estimate is a piecewise constant function defined on a binary partition of Ω. The key ingredient of the algorithm is to use discrepancy, a concept origina...