This paper investigates nonparametric estimations of a density function within a mixed density model. A linear wavelet density estimator and an adaptive nonlinear wavelet estimator are proposed using wavelet method and hard thresholding algorithm. Un...
We present a novel nonparametric adaptive partitioning and stitching (NAPS) algorithm to estimate a probability density function (PDF) of a single variable. Sampled data is partitioned into blocks using a branching tree algorithm that minimizes devia...
Estimation of probability density functions (pdf) is considered an essential part of statistical modelling. Heteroskedasticity and outliers are the problems that make data analysis harder. The Cauchy mixture model helps us to cover both of them. This...
We consider a rather general problem of nonparametric estimation of an uncountable set of probability density functions (p.d.f.’s) of the form: f ( x ; r ) , where r is a non-random real variable and ranges from R 1 to R 2...
This paper proposes several methodologies whose objective consists of securing copula density estimates. More specifically, this aim will be achieved by differentiating bivariate least-squares polynomials fitted to Deheuvels’ empirical copulas,...
Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive nume...
Nonparametric estimation for a probability density function that describes multivariate data has typically been addressed by kernel density estimation (KDE). A novel density estimator recently developed by Farmer and Jacobs offers an alternative high...
The article investigates the accuracy of nonparametric univariate density estimation methods applied to various Gaussian mixture models. A comprehensive comparative analysis is performed for four popular estimation approaches: adaptive kernel density...
This work is concerned with multivariate conditional heteroscedastic autoregressive nonlinear (CHARN) models with an unknown conditional mean function, conditional variance matrix function and density function of the distribution of noise. We study t...
Estimating the Probability Density Function (PDF) of observed data is crucial as a problem in its own right, and also for diverse engineering applications. This paper utilizes two powerful mathematical tools, the concept of moments and the relatively...
The uncertainty of wind power brings many challenges to the operation and control of power systems, especially for the joint operation of multiple wind farms. Therefore, the study of the joint probability density function (JPDF) of multiple wind farm...
At the heart of many ICA techniques is a nonparametric estimate of an information measure, usually via nonparametric density estimation, for example, kernel density estimation. While not as popular as kernel density estimators, orthogonal functions c...
The properties of non-parametric kernel estimators for probability density function from two special classes are investigated. Each class is parametrized with distribution smoothness parameter. One of the classes was introduced by Rosenblatt, another...
Previously, we developed a high throughput non-parametric maximum entropy method (PLOS ONE, 13(5): e0196937, 2018) that employs a log-likelihood scoring function to characterize uncertainty in trial probability density estimates through a scaled quan...
We address the problem of non-parametric estimation of the recently proposed measures of statistical dispersion of positive continuous random variables. The measures are based on the concepts of differential entropy and Fisher information and describ...
To address the issue of uncertainty in renewable energy and its impact on the safe and stable operation of power systems, this paper proposes a transient stability constrained optimal power flow (TSCOPF) calculation method that takes into account the...
The creation and maintenance of complex forest structures has become an important forestry objective. Complex forest structures, often expressed in multimodal shapes of tree size/diameter (DBH) distributions, are challenging to model. Mixture probabi...
The use of a metric to assess distance between probability densities is an important practical problem. In this work, a particular metric induced by an α-divergence is studied. The Hellinger metric can be interpreted as a particular case within the f...
This work studies the underwater detection and tracking of diver targets under a low signal-to-reverberation ratio (SRR) in active sonar systems. In particular, a particle filter track-before-detect based on a knowledge-aided (KA-PF-TBD) algorithm is...
Large-scale grid integration of renewable energy increases the uncertainty and volatility of power systems, which brings difficulties to output planning and reserve decision-making of power system units. In this paper, we innovatively combined the no...
The traditional optimization scheduling of distribution networks has often only considered the volatility and randomness of wind and solar output. When estimating the prediction errors of wind and solar output, wind turbines and photovoltaics are typ...
In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficient when the parametric family contains the data-genera...
Accurately quantifying the size–density relationships is important to predict stand development, estimate stand carrying capacity and prescribe silvicultural treatments. Parametric methods, such as segmented regression, were proposed to estimat...
The account of total biomass can assist with the evaluation of climate regulation policies from local to global scales. This study estimates total biomass (TB), including tree and shrub biomass fractions, in Pinus halepensis Miller forest stands loca...
This paper develops a method to obtain multivariate kernel functions for density estimation problems in which the density function is defined on compact support. If domain-specific knowledge requires certain conditions to be satisfied at the boundary...
In this article, we examine a class of partially linear additive models (PLAM) defined via a measurable mapping Ψ:Rq→R. More precisely, we consider Ψ(Yi):=Yi=Zi⊤β+∑l=1dml(Xl,i)+εi,i=1,…,n, where Zi=(Zi,1,&he...
Medical diagnosis is the basis for treatment and management decisions in healthcare. Conventional methods for medical diagnosis commonly use established clinical criteria and fixed numerical thresholds. The limitations of such an approach may result...
Using information-theoretic quantities in practical applications with continuous data is often hindered by the fact that probability density functions need to be estimated in higher dimensions, which can become unreliable or even computationally unfe...
Data clustering is one area of data mining that falls into the data mining class of unsupervised learning. Cluster analysis divides data into different classes by discovering the internal structure of data set objects and their relationship. This pap...
Unsupervised learning is one type of machine learning with an exceptionally high number of applications in various fields. The most popular and best-known group of unsupervised machine learning methods is clustering methods. The main goal of clusteri...
River runoff simulation and prediction are important for controlling the water volume and ensuring the optimal allocation of water resources in river basins. However, the instability of medium- and long-term runoff series increases the difficulty of...
Over the past few years, we have seen an increased need to analyze the dynamically changing behaviors of economic and financial time series. These needs have led to significant demand for methods that denoise non-stationary time series across time an...
In recent years, the global electric vehicle (EV) sector has experienced rapid growth, resulting in major load variations in microgrids due to uncontrolled charging behaviors. Simultaneously, the unpredictable nature of distributed energy output comp...
With the increasing permeability of photovoltaic (PV) power production, the uncertainties and randomness of PV power have played a critical role in the operation and dispatch of the power grid and amplified the abandon rate of PV power. Consequently,...
Scatter plots of multivariate data sets motivate modeling of star-shaped distributions beyond elliptically contoured ones. We study properties of estimators for the density generator function, the star-generalized radius distribution and the density...
This paper develops a sampling algorithm for bandwidth estimation in a nonparametric regression model with continuous and discrete regressors under an unknown error density. The error density is approximated by the kernel density estimator of the uno...
Some authors have recently warned about the risks of the sentence with enough data, the numbers speak for themselves. The problem of nonparametric statistical inference in big data under the presence of sampling bias is considered in this work. The m...
Low-lying coastal communities are often threatened by compound flooding (CF), which can be determined through the joint occurrence of storm surges, rainfall and river discharge, either successively or in close succession. The trivariate distribution...
Bootstrap methods are used for bandwidth selection in: (1) nonparametric kernel density estimation with dependent data (smoothed stationary bootstrap and smoothed moving blocks bootstrap), and (2) nonparametric kernel hazard rate estimation (smoothed...
This paper proposes a semiparametric realized stochastic volatility model by integrating the parametric stochastic volatility model utilizing realized volatility information and the Bayesian nonparametric framework. The flexible framework offered by...
In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier tra...
The paper proposes a new non-parametric density estimator from region-censored observations with application in the context of population studies, where standard maximum likelihood is affected by over-fitting and non-uniqueness problems. It is a maxi...
In this work, we prove the convergence to 0 in both L1 and L2 of the Bayes estimator of a regression curve (i.e., the conditional expectation of the response variable given the regressor). The strong consistency of the estimator is also derived. The...
Let fn be the non-parametric kernel density estimator based on a kernel function K and a sequence of independent and identically distributed random vectors taking values in Rd. With some mild conditions, we establish sharp moderate deviations for the...
Kernel density estimation is a non-parametric method to estimate the probability density function of a random quantity from a finite data sample. The estimator consists of a kernel function and a smoothing parameter called the bandwidth. Despite its...
Considering the impact of the number of potential new coronavirus infections in each city, this paper explores the relationship between temperature and cumulative confirmed cases of COVID-19 in mainland China through the non-parametric method. In thi...
A method is described for the calculation of the three-parameter Weibull distribution function from censored samples. The method introduces a data driven technique based on an adapted Gaussian like kernel to match the censoring scheme. The method min...
This paper proposes a genetic algorithm-based Markov Chain approach that can be used for non-parametric estimation of regression coefficients and their statistical confidence bounds. The proposed approach can generate samples from an unknown probabil...
Uncertainty of greenhouse gas (GHG) emissions was analyzed using the parametric Monte Carlo simulation (MCS) method and the non-parametric bootstrap method. There was a certain number of observations required of a dataset before GHG emissions reached...
Atmospheric Lagrangian particle dispersion models, LPDM, simulate the dispersion of passive tracers in the atmosphere. At the most basic level, model output consists of the position of computational particles and the amount of mass they represent. In...
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