Related papers: Data-driven density derivative estimation, with ap…
Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…
This paper presents a Bayesian sampling approach to bandwidth estimation for the local linear estimator of the regression function in a nonparametric regression model. In the Bayesian sampling approach, the error density is approximated by…
Standard Mean-Shift algorithms are notoriously sensitive to the bandwidth hyperparameter, particularly in data-scarce regimes where fixed-scale density estimation leads to fragmentation and spurious modes. In this paper, we propose Doubly…
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…
The performance of multivariate kernel density estimation (KDE) depends strongly on the choice of bandwidth matrix. The high computational cost required for its estimation provides a big motivation to develop fast and accurate methods. One…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a…
We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating relationship between a response variable and its covariates. Specifically, modal regression…
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous…
Hidden Markov models and their variants are the predominant sequential classification method in such domains as speech recognition, bioinformatics and natural language processing. Being generative rather than discriminative models, however,…
The density ratio is an important metric for evaluating the relative likelihood of two probability distributions, with extensive applications in statistics and machine learning. However, existing estimation theories for density ratios often…
This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…
Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns.…
We discuss and compare various approaches to the problem of bandwidth selection for kernel estimators of intensity functions of spatial point processes. We also propose a new method based on the Campbell formula applied to the reciprocal…
A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative…
Dirichlet process mixture model (DPMM) is a popular Bayesian nonparametric model. In this paper, we apply this model to weighted data and then estimate the un-weighted distribution from the corresponding weighted distribution using the…