Nonparametric Density Research Articles

Generalized accelerated failure time model with censored data from case-cohort studies

The case-cohort design is a cost-effective approach commonly used in large cohort studies. Under this design, covariates are collected only for the cases and a small subcohort randomly selected from the entire cohort. In this paper, we consider a flexible generalized accelerated failure time model for fitting case-cohort data. A weighted estimating procedure is proposed and the corresponding asymptotic properties of the resulting estimator are established. Two efficient resampling-based inference procedures which do not involve nonparametric density estimation or numerical derivatives are suggested. The finite sample performance of the proposed estimators is evaluated by simulation studies. Also, a real example is used to demonstrate the application of the proposed methods.

AUTOMATIC BUILDING FOOTPRINT EXTRACTION FROM 3D LASERSCANS

Abstract. Building footprints are a prerequisite for many tasks such as urban mapping and planning. Such structures are mostly derived using airborne laser scanning which reveals rather roof structures than the underlying hidden footprint boundary. This paper introduces an approach to extract a 2D building boundary from a 3D point cloud stemming from either terrestrial scanning or via close-range sensing using a mobile platform, e.g. drone. To this end, a pipeline of methods including non-parametric kernel density estimation (KDE) of an underlying probability density function, a solution of the Travelling Salesperson Problem (TSP), outlier elimination and line segmentation are presented to extract the underlying building footprint. KDE turns out to be suitable to automatically determine a horizontal cut in the point cloud. An ordering of the resulting points in this cut using a shortest possible tour based on TSP allows for the application of existing line segmentation algorithms, otherwise dedicated to indoor segmentation. Outliers in the resulting segments are removed using Density-Based Spatial Clustering of Applications with Noise (DBSCAN). The segments are then generalized leading to the final footprint geometry. We applied our approach on real-world examples and achieved an IoU between 0.930 and 0.998 assessed by ground truth footprints from both authoritative and volunteered geographic information (VGI) data.

Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis

The joint probability modelling of storm surges and rainfall events is the main task in assessing compound flood risk in low-lying coastal areas. These extreme or non-extreme events may not be dangerous if considered individually but can intensify flooding impact if they occur simultaneously or successively. Recently, the copula approach has been widely accepted in compound flooding but is often limited to parametric or semiparametric distribution settings in a limited number of cases. However, both parametric and semiparametric approaches assume the prior distribution type for univariate marginals and copula joint density. In that case, there is a high risk of misspecification if the underlying assumption is violated. In addition, both approaches suffer from a lack of flexibility. This study uses bivariate copula density in the nonparametric distribution setting. The joint copula structure is approximated nonparametrically by employing the Bernstein copula estimator and Beta kernel copula density, and their performances are also compared. The proposed model is tested with 46 years of rainfall and storm surge observations collected on Canada's west coast. The marginal distribution of the selected flood variables is modelled using nonparametric kernel density estimation (KDE). Based on the different model compatibility tests, the Bernstein copula with normal KDE margins defined the joint dependence structure well. The selected nonparametric copula model is further employed to estimate joint and conditional return periods. It is found that flood hazard characteristics occurrence simultaneously is less frequent in AND-joint cases than in OR-joint cases. Also, the derived model is further used to estimate failure probability (FP) statistics to assess the variation of bivariate hydrologic risk during the project lifetime. It is found that FP statistics could be underestimated when neglecting the compound effect of storm surge and rainfall in the coastal flood risk.

PDFEstimator: An R Package for Density Estimation and Analysis

This article presents PDFEstimator, an R package for nonparametric probability density estimation and analysis, as both a practical enhancement and alternative to kernel-based estimators. PDFEstimator creates fast, highly accurate, data-driven probability density estimates for continuous random data through an intuitive interface. Excellent results are obtained for a diverse set of data distributions ranging from 10 to $10^6$ samples when invoked with default parameter definitions in the absence of user directives. Additionally, the package contains methods for assessing the quality of any estimate, including robust plotting functions for detailed visualization and trouble-shooting. Usage of PDFEstimator is illustrated through a variety of examples, including comparisons to several kernel density methods.

Characterization of complex fluvial-deltaic deposits in Northeast India using Poisson impedance inversion and non-parametric statistical technique

Characterizing complex fluvial-deltaic deposits is a challenging task for finding hydrocarbon discoveries. We described a methodology for predicting the hydrocarbon zones from complex well-log and prestack seismic data. In this current study, data analysis involves an integrated framework based on Simultaneous prestack seismic inversion (SPSI), target correlation coefficient analysis (TCCA), Poisson impedance inversion, and non-parametric statistical analysis, and Bayesian classification. First, seismic elastic attributes from prestack seismic data were estimated. They can provide the spatial distribution of petrophysical properties of seismic data. Then target correlation coefficient analysis (TCCA) was estimated roration factor “c” from well-log data. Using the seismic elastic attributes and rotation factor “c”, Poisson impedance inversion was performed to predict the Poisson impedance volume. Finally, Bayesian classification integrated the Poisson impedance volume with non-parametric probabilistic density functions (PDFs) to estimate the spatial distribution of lithofacies. Despite complex characteristics in the elastic properties, the current study successfully delineated the complex fluvial-details deposits. These results were verified with conventional findings through numerical analysis.

An integrated approach for identification and quantification of ecological drought in rivers from an ecological streamflow perspective

Although various studies have investigated the impacts of climate variability and human activities on drought, researches specifically analysing the impact on ecological drought are still limited. A deep understanding of the climatic and anthropogenic effects on ecological drought processes is crucial for ecological regulation and management in the changing environments. In the present study, an integrated approach for comprehensive understanding and quantification of ecological drought in rivers was proposed which first applied the nonparametric kernel density estimation (KDE) method to calculate the most suitable ecological streamflow (MSES) for a river ecosystem. Then, the variable threshold level method based on the MSES for each month and the run theory method were applied to identify the ecological drought duration and deficit volumes. Finally, a quantification approach based on hydrological model simulation was proposed to attribute the impacts of climate variability and human activities on ecological drought. The proposed approach was applied on two catchments, Xianyang (XY) and Huaxian (HX) within the Weihe River Basin (WRB) in northern China. Comparison results obtained using the two empirical methods revealed that the MSES calculated using the KDE method was reasonable and can be used for ecological drought identification. The identification results showed that both the median and upper quartile values of the drought duration and deficit volumes during the disturbed period (1991–2017) were greater than those during the undisturbed period (1961–1990). Quantification results showed that human activities were the dominant factor aggravating ecological drought in the WRB after 1990. The contribution rates of climate variability and human activities toward ecological drought variations were 25.6% and 74.4%, respectively, for the XY station and 42.7% and 57.3%, respectively, for the HX station. Although the WRB was selected as a case study, the proposed approach can also be applied to other regions to provide scientific guidance for regional ecological management.

Extra credit for disruption: trend of disruption in radiology academic journals

To identify the most disruptive publications, which are those that are cited more frequently than their own references, in academic radiology journals and their characteristics, such as the number of authors and relative time to publication. A comprehensive literature search was undertaken to identify the 100 most disruptive publications in the field of radiology. Subsequently, statistical analysis was applied to establish the distribution of disruptive scores of the isolated publications using a non-parametric probability density function. The relation between disruptive scores and citation counts was then determined, with the aid of a correlation coefficient. Finally, data regarding any significant connection between disruption scores and time of publication, number of authors, and study design were examined. Analysing the top 100 papers in increments of 10-year periods showed no significant difference in the distribution of disruption scores over time. No correlation between an article's citation count and disruption score was established. Additionally, no significant relation between the number of authors/study design and disruption scores was identified. The disruption score highlights significant impact elements not entirely accounted for by citation count. Its potential benefit in assessing scientific impact should be contemplated.

Estimation and Dynamic Evolution of Provincial Factor-Output Elasticity in China

China is currently in a new phase of transition from high-speed growth to high-quality growth, and accurate estimation of element outputs is essential for the smooth progress of the transition. Using the back-fitting method, this study constructed a model of a spatiotemporal-varying elasticity production function to estimate the factor-output elasticity from 1993 to 2017 in 31 Chinese provinces. Nonparametric kernel density method was applied to describe the spatiotemporal evolution characteristics of factor-output elasticity. The results show that the factor-output elasticity of different provinces shows a nonlinear change trend over time and between regions. Overall, the elasticity of labor output shows a decreasing trend, the elasticity of capital output shows an increasing tendency, the eastern region has the lowest level of labor-output elasticity, but the highest level of capital-output elasticity. The western region has the highest level of labor-output elasticity but the lowest level of capital-output elasticity. On the whole, regions with higher resilience in labor output gradually shift towards the West, while capital shifts towards the East.

GENs: generative encoding networks

Mapping data from and/or onto a known family of distributions has become an important topic in machine learning and data analysis. Deep generative models (e.g., generative adversarial networks) have been used effectively to match known and unknown distributions. Nonetheless, when the form of the target distribution is known, analytical methods are advantageous in providing robust results with provable properties. In this paper, we propose and analyze the use of nonparametric density methods to estimate the Jensen-Shannon divergence for matching unknown data distributions to known target distributions, such Gaussian or mixtures of Gaussians, in latent spaces. This analytical method has several advantages: better behavior when training sample quantity is low, provable convergence properties, and relatively few parameters, which can be derived analytically. Using the proposed method, we enforce the latent representation of an autoencoder to match a target distribution in a learning framework that we call a generative encoding network. Here, we present the numerical methods for bandwidth estimation; derive the expected distribution of the data in the latent space; show the advantages over the adversarial counterpart; study the properties of the latent space such as entropy, sample generation, interpolation; and demonstrate the application of the method in the real world.

Flexible semiparametric mode regression for time-to-event data.

The distribution of time-to-event outcomes is usually right-skewed. While for symmetric and moderately skewed data the mean and median are appropriate location measures, the mode is preferable for heavily skewed data as it better represents the center of the distribution. Mode regression has been introduced for uncensored data to model the relationship between covariates and the mode of the outcome. Starting from nonparametric kernel density based mode regression, we examine the use of inverse probability of censoring weights to extend mode regression to handle right-censored data. We add a semiparametric predictor to add further flexibility to the model and we construct a pseudo Akaike's information criterion to select the bandwidth and smoothing parameters. We use simulations to evaluate the performance of our proposed approach. We demonstrate the benefit of adding mode regression to one's toolbox for analyzing survival data on a pancreatic cancer data set from a prospectively maintained cancer registry.

Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations

We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic smoothness assumptions on the unknown functions. The analysis is based on continuous observations of the process, and the estimators’ performance is measured in terms of the sup-norm loss. Regarding invariant density estimation, we obtain highly nonclassical results for the rate of convergence, which reflect the inhomogeneous variance structure of the process. Concerning estimation of the drift vector, we suggest both non-adaptive and fully data-driven procedures. All of the aforementioned results strongly rely on tight uniform moment bounds for empirical processes associated to deterministic and stochastic integrals of the investigated process, which are also proven in this paper.

Investigation of the statistical fluctuations of the electric quadrupole transition rates of spherical nuclei by kernel density estimation method‎

In this study, the statistical correlation of the electric quadrupole transition probabilities in the spherical nuclei is investigated. To this aim, the spherical even-even nuclei in the 100 < A < 126 mass region are selected and the electric quadrupole transition rates of different levels in the ground band are determined by the interacting boson model in the U(5) dynamical limit. A non-parametric kernel density estimation method is used in the framework of nearest neighbor spacing distribution of random matrix theory to consider the statistical correlation of these quadrupole transition rates. Also, the Kullback-Leibler divergence is used to describe the regular or chaotic behavior of the considered sequences. The results show the correlation of the electric quadrupole transition probabilities between different levels of the ground band. Also, the correlation increased for such transitions that the angular momentum of the initial state of quadrupole transitions increased.

Robust Under-Frequency Load Shedding With Electric Vehicles Under Wind Power and Commute Uncertainties

Under-frequency load shedding (UFLS) is an important measure for tackling low-frequency events caused by load-generation imbalance. However, the uncertainty of wind power amplifies power imbalances and can potentially impair frequency stability. Electric vehicles (EVs) present a more effective means for addressing this issue compared to load shedding. However, EVs have several limitations such as commute randomness. To ensure frequency stability and simultaneously reduce load shedding, a bi-level confidence-interval-based optimal strategy is proposed to enable the participation of EVs in UFLS, where the uncertainties of wind power and the commute randomness of EVs are estimated using a non-parametric kernel density estimation (KDE) method. In bi-level optimization, the upper level reduces the dependency on commute randomness and the wind power uncertainty during load-shedding events. Further, the upper-level solutions are sent to EV charging stations for emergency dispatch. By contrast, at the lower level, an approximation-function-based priority is proposed to optimize the task allocation. Simulation results show the advantages of the proposed approach in maintaining a stable frequency compared with traditional and adaptive UFLS schemes.

Probabilistic Day-Ahead Inertia Forecasting

Power system inertia is declining and is increasingly variable and uncertain in regions where the penetration of non-synchronous generation and interconnectors is growing. This presents a challenge to power system operators who must take appropriate actions to ensure the stability and security of power systems relying on short-term forecasts of the system’s inertial response. Existing models to forecast inertia fail to quantify uncertainty, which may prevent their utilization given the risk aversion of the system operators when handling stability issues. This paper is the first to develop a model to produce calibrated, data-driven probabilistic forecasts of the inertia contribution of transmission-connected synchronous generators. The model provides a necessary tool for system operators to quantify forecast uncertainty, allowing them to manage the risk of frequency instability cost-effectively. The paper demonstrates that the assumption of a Gaussian distribution of uncertainty applied in existing models is not acceptable to accurately forecast the inertial response and provides a satisfactory forecast model by combining non-parametric density forecasting with parametric tail distributions. Moreover, the paper shows that satisfactory predictive performance can only be achieved by adopting a rolling horizon forecast approach to deal with the rapidly changing characteristics of the inertial response in power systems.

Correction: Nonparametric conditional density estimation in a deep learning framework for short-term forecasting

Correction: Nonparametric conditional density estimation in a deep learning framework for short-term forecasting

New classification method of coal spontaneous combustion three zones in the goaf based on non-parametric kernel density estimation.

The accurate division of three zones of coal spontaneous combustion in the goaf plays a vital role for coal fire prevention. Based on the O2 and CO volume fraction acquired from in situ test, this paper first fits the linear equation (characteristic equation) of O2 volume fraction with the length of the goaf. Then a cloud map of the kernel density distribution of O2 and CO volume fraction and the length of the goaf was drawn. According to the cloud map of CO, the distribution interval of CO volume fraction can be obtained, in which 0-100 ppm is the acceptable range, and greater than 100 ppm is the dangerous range, which can be used as a critical indicator for early warning of coal spontaneous combustion. According to the kernel density distribution cloud map of O2 volume fraction, there are 3 peaks of the kernel density of O2 volume fraction. According to the difference test, the 3 goaf lengths (characteristic lengths) corresponding to the 3 kernel density peaks are determined to be 12 m, 34 m, and 59 m, respectively. The characteristic O2 volume fractions are obtained by substituting characteristic lengths into the characteristic equation, which are 17.9%, 13.6%, and 8.9%. Different from the traditional dividing method, the characteristic O2 volume fractions and characteristic lengths divide the goaf into four areas: the heat dissipation zone, the first oxidation zone, the second oxidation zone, and the asphyxiation zone. The results of this study could refine the division of coal spontaneous combustion dangerous areas, reflect the dynamic change process of coal spontaneous combustion dangerous areas, and improve the efficiency of coal spontaneous combustion prevention.

A Bayesian based approach for analyzing customer’s online sales data to identify weights of product attributes

E-commerce websites include large volume of online customer data regarding customer preferences. This study puts forward a novel Bayesian methodology to estimate the impact of product attributes on customer satisfaction by analyzing online data, so that product designers and market researchers are facilitated in their decision making processes. This method proves that valuable information on customer insights can be provided even if we have only data of overall customer satisfaction score and product attribute characteristics. The unknown data are acquired via statistical methods such that non-parametric density estimation is utilized to estimate distributions of satisfaction scores of product attributes. The impacts of product attributes on customer satisfaction are considered as weights of mixture kernel distributions and posterior distributions of weights are simulated with Markov Chain Monte Carlo method. The applicability of the proposed methodology is demonstrated by a case study, in which online data of mobile phone market are analyzed.

Spatio-temporal dynamic evolution of carbon emission intensity and the effectiveness of carbon emission reduction at county level based on nighttime light data

Accelerating carbon emission reduction is conducive to protecting the ecological security of the Qinghai-Tibet Plateau. Based on a case study of 41 counties in Qinghai Province, China, this study explored the characteristics regarding the spatio-temporal dynamic evolution of carbon emission intensity (CEI) by using the nonparametric kernel density estimation, spatial Markov chain , and spatial variogram model and used the corrective coefficient to examine the effectiveness of the decrease of CEI. The main conclusions are as follows: First, the CEI of most counties showed a decreasing trend, although a few counties exhibited unstable CEI increase through the study period. Second, county-level changes in CEI exhibited club convergence and spatial correlation , and the county-level spatial differences in CEI narrowed. Finally, the decrease of CEI in some counties was lower than the provincial average suggesting that, even at the provincial level, the principle of common but differentiated responsibility should be observed when promoting carbon emission reduction. This study provides several recommendations to promote the sustainable development of Qinghai Province.

Real-time remaining useful life prediction based on adaptive kernel window width density

Remaining useful life (RUL) prediction plays an important role in improving the availability and productivity of systems. To improve the accuracy of real-time RUL prediction during system operation, we propose a modeling method for real-time RUL prediction based on adaptive kernel window width density. First, a non-parametric kernel density estimation (KDE) real-time RUL prediction model is proposed, and a window width model with adaptive kernel window width density is established by introducing a local density factor in the window width selection. The local density of sample points is calculated by the k-nearest neighbor distance, and the KDE is performed by adaptively selecting the window width value according to the local density of sample points in the region of non-uniform distribution of sample points. As the monitoring data changes in real time, the kernel density estimates of known samples are used to recursively update the kernel density estimates of new samples. Moreover, the logarithmic transformation of random variables and space mapping are used in the establishment of the RUL prediction model. A model of logarithmic kernel diffeomorphism transformation is established to solve the boundary shift problem of kernel estimation in the prediction to improve the prediction accuracy. Finally, the validity of the method is verified through case studies, and the accuracy of the model is judged using evaluation quasi-measures.

Time sequence probabilistic influence of traction load with small sample of newly high-speed railway on power grid

More and more traction stations of new high-speed railway are connected to the power grid, and the major challenges to the power grid has been brought. This paper proposes a probabilistic method for the timing influence of traction load with small sample on power grid based on non-parametric Bootstrap and kernel density estimation. Firstly, in view of the small sample problem of traction load test data, the timing samples of traction load of are obtained using the non-parametric Bootstrap. Secondly, the equivalent three-phase model of the traction power supply system is obtained through the voltage/current transformation matrix of the traction transformer. The three-phase power flow calculation model of the power system with traction load is established. Then, the three-phase time sequence probabilistic power flow is calculated by the Monte Carlo simulation, and the Kernel density estimation (KDE) is used to calculate the probability distribution of output random variable. Finally, the timing influence of traction load on the voltage amplitude and unbalance degree of grid nodes are analysed by the modified IEEE-14 bus three-phase system. The simulation results verify the effectiveness of the proposed method.