Related papers: Fused Density Estimation: Theory and Methods
Asymptotic properties of three estimators of probability density function of sample maximum $f_{(m)}:=mfF^{m-1}$ are derived, where $m$ is a function of sample size $n$. One of the estimators is the parametrically fitted by the…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the…
We study the problem of estimating the probability density function of a circular random variable subject to censoring. To this end, we propose a fully computable quotient estimator that combines a projection estimator on linear sieves with…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
We consider the non-parametric maximum likelihood estimation in the class of Polya frequency functions of order two, viz. the densities with a concave logarithm. This is a subclass of unimodal densities and fairly rich in general. The NPMLE…
As a fundamental information fusion approach, the arithmetic average (AA) fusion has recently been investigated for various random finite set (RFS) filter fusion in the context of multi-sensor multi-target tracking. It is not a…
With the recent growth in data availability and complexity, and the associated outburst of elaborate modelling approaches, model selection tools have become a lifeline, providing objective criteria to deal with this increasingly challenging…
We present an analysis of optimal quantization of probability measures with nonuniform densities on spherical curves. We begin by deriving the centroid condition, followed by a high-resolution asymptotic analysis to establish the…
Multi-modal densities appear frequently in time series and practical applications. However, they cannot be represented by common state estimators, such as the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF), which…
In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation…
Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the \emph{mixing measure}, a fundamental object…
Spectral density matrix estimation of multivariate time series is a classical problem in time series and signal processing. In modern neuroscience, spectral density based metrics are commonly used for analyzing functional connectivity among…
We study the problem of variance estimation in general graph-structured problems. First, we develop a linear time estimator for the homoscedastic case that can consistently estimate the variance in general graphs. We show that our estimator…
Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical…
In this paper, we propose a density estimation algorithm called \textit{Gradient Boosting Histogram Transform} (GBHT), where we adopt the \textit{Negative Log Likelihood} as the loss function to make the boosting procedure available for the…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
In this paper, we propose a theoretical analysis of the algorithm ISDE, introduced in previous work. From a dataset, ISDE learns a density written as a product of marginal density estimators over a partition of the features. We show that…