A Non-Parametric Scheme for Identifying Data Characteristic Based on Curve Similarity Matching

For accurately identifying the distribution charac-teristic of Gaussian-like noises in unmanned aerial vehicle(UAV)state estimation,this paper proposes a non-parametric scheme based on curve similarity matching.In the framework of the pro-posed scheme,a Parzen window(kernel density estimation,KDE)method on sliding window technology is applied for roughly esti-mating the sample probability density,a precise data probability density function(PDF)model is constructed with the least square method on K-fold cross validation,and the testing result based on evaluation method is obtained based on some data characteristic analyses of curve shape,abruptness and symmetry.Some com-parison simulations with classical methods and UAV flight exper-iment shows that the proposed scheme has higher recognition accuracy than classical methods for some kinds of Gaussian-like data,which provides better reference for the design of Kalman filter(KF)in complex water environment.

Comparison of Type I Error Rates of Siegel-Tukey and Savage Tests among Non-Parametric Tests

This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.

A non-parametric indicator Kriging method for generating coastal sediment type map

Coastal sediment type map has been widely used in marine economic and engineering activities, but the traditional mapping methods had some limitations due to their intrinsic assumption or subjectivity. In this paper, a non-parametric indicator Kriging method has been proposed for generating coastal sediment map. The method can effectively avoid mapping subjectivity, has no special requirements for the sample data to meet second-order stationary or normal distribution, and can also provide useful information on the quantitative evaluation of mapping uncertainty. The application of the method in the southern sea area of Lianyungang showed that much more convincing mapping results could be obtained compared with the traditional methods such as IDW, Kriging and Voronoi diagram under the same condition, so the proposed method was applicable with great utilization value.

A Short-Term Traffic Flow Forecasting Method Based on a Three-Layer K-Nearest Neighbor Non-Parametric Regression Algorithm

Short-term traffic flow is one of the core technologies to realize traffic flow guidance. In this article, in view of the characteristics that the traffic flow changes repeatedly, a short-term traffic flow forecasting method based on a three-layer K-nearest neighbor non-parametric regression algorithm is proposed. Specifically, two screening layers based on shape similarity were introduced in K-nearest neighbor non-parametric regression method, and the forecasting results were output using the weighted averaging on the reciprocal values of the shape similarity distances and the most-similar-point distance adjustment method. According to the experimental results, the proposed algorithm has improved the predictive ability of the traditional K-nearest neighbor non-parametric regression method, and greatly enhanced the accuracy and real-time performance of short-term traffic flow forecasting.

An Improved Non-Parametric Method for Multiple Moving Objects Detection in the Markov Random Field

Detecting moving objects in the stationary background is an important problem in visual surveillance systems.However,the traditional background subtraction method fails when the background is not completely stationary and involves certain dynamic changes.In this paper,according to the basic steps of the background subtraction method,a novel non-parametric moving object detection method is proposed based on an improved ant colony algorithm by using the Markov random field.Concretely,the contributions are as follows:1)A new nonparametric strategy is utilized to model the background,based on an improved kernel density estimation;this approach uses an adaptive bandwidth,and the fused features combine the colours,gradients and positions.2)A Markov random field method based on this adaptive background model via the constraint of the spatial context is proposed to extract objects.3)The posterior function is maximized efficiently by using an improved ant colony system algorithm.Extensive experiments show that the proposed method demonstrates a better performance than many existing state-of-the-art methods.

Exponential Continuous Non-Parametric Neural Identifier With Predefined Convergence Velocity

This paper addresses the design of an exponential function-based learning law for artificial neural networks(ANNs)with continuous dynamics.The ANN structure is used to obtain a non-parametric model of systems with uncertainties,which are described by a set of nonlinear ordinary differential equations.Two novel adaptive algorithms with predefined exponential convergence rate adjust the weights of the ANN.The first algorithm includes an adaptive gain depending on the identification error which accelerated the convergence of the weights and promotes a faster convergence between the states of the uncertain system and the trajectories of the neural identifier.The second approach uses a time-dependent sigmoidal gain that forces the convergence of the identification error to an invariant set characterized by an ellipsoid.The generalized volume of this ellipsoid depends on the upper bounds of uncertainties,perturbations and modeling errors.The application of the invariant ellipsoid method yields to obtain an algorithm to reduce the volume of the convergence region for the identification error.Both adaptive algorithms are derived from the application of a non-standard exponential dependent function and an associated controlled Lyapunov function.Numerical examples demonstrate the improvements enforced by the algorithms introduced in this study by comparing the convergence settings concerning classical schemes with non-exponential continuous learning methods.The proposed identifiers overcome the results of the classical identifier achieving a faster convergence to an invariant set of smaller dimensions.

Non-parametric camera calibration method using single-axis rotational target

The ability to build an imaging process is crucial to vision measurement.The non-parametric imaging model describes an imaging process as a pixel cluster,in which each pixel is related to a spatial ray originated from an object point.However,a non-parametric model requires a sophisticated calculation process or high-cost devices to obtain a massive quantity of parameters.These disadvantages limit the application of camera models.Therefore,we propose a novel camera model calibration method based on a single-axis rotational target.The rotational vision target offers 3D control points with no need for detailed information of poses of the rotational target.Radial basis function(RBF)network is introduced to map 3D coordinates to 2D image coordinates.We subsequently derive the optimization formulization of imaging model parameters and compute the parameter from the given control points.The model is extended to adapt the stereo camera that is widely used in vision measurement.Experiments have been done to evaluate the performance of the proposed camera calibration method.The results show that the proposed method has superiority in accuracy and effectiveness in comparison with the traditional methods.

Bayesian Non-Parametric Mixture Model with Application to Modeling Biological Markers

The effect of treatment on patient’s outcome can easily be determined through the impact of the treatment on biological events. Observing the treatment for patients for a certain period of time can help in determining whether there is any change in the biomarker of the patient. It is important to study how the biomarker changes due to treatment and whether for different individuals located in separate centers can be clustered together since they might have different distributions. The study is motivated by a Bayesian non-parametric mixture model, which is more flexible when compared to the Bayesian Parametric models and is capable of borrowing information across different centers allowing them to be grouped together. To this end, this research modeled Biological markers taking into consideration the Surrogate markers. The study employed the nested Dirichlet process prior, which is easily peaceable on different distributions for several centers, with centers from the same Dirichlet process component clustered automatically together. The study sampled from the posterior by use of Markov chain Monte carol algorithm. The model is illustrated using a simulation study to see how it performs on simulated data. Clearly, from the simulation study it was clear that, the model was capable of clustering data into different clusters.

Analysis of Trends in Drought with the Non-Parametric Approach in Vietnam: A Case Study in Ninh Thuan Province

A quantitative study was used in the study of the tendency to change drought indicators in Vietnam through the Ninh Thuan province case study. The research data are temperature and precipitation data of 11 stations from 1986 to 2016 inside and outside Ninh Thuan province. To do the research, the author uses a non-parametric analysis method and the drought index calculation method. Specifically, with the non-parametric method, the author uses the analysis, Mann-Kendall (MK) and Theil-Sen (Sen’s slope), and to analyze drought, the author uses the Standardized Precipitation Index (SPI) and the Moisture Index (MI). Two Softwares calculated in this study are ProUCL 5.1 and MAKENSEN 1.0 by the US Environmental Protection Agency and Finnish Meteorological Institute. The calculation results show that meteorological drought will decrease in the future with areas such as Phan Rang, Song Pha, Quan The, Ba Thap tend to increase very clearly, while Tam My and Nhi Ha tend to increase very clearly short. With the agricultural drought, the average MI results increased 0.013 per year, of which Song Pha station tended to increase the highest with 0.03 per year and lower with Nhi Ha with 0.001 per year. The forecast results also show that by the end of the 21st century, the SPI tends to decrease with SPI 1 being −0.68, SPI 3 being −0.40, SPI 6 being −0.25, SPI 12 is 0.42. Along with that is the forecast that the MI index will increase 0.013 per year to 2035, the MI index is 0.93, in 2050 it is 1.13, in 2075 it will be 1.46, and by 2100 it is 1.79. Research results will be used in policymaking, environmental resources management agencies, and researchers to develop and study solutions to adapt and mitigate drought in the context of variable climate change.

Oxygen uptake response to switching stairs exercise by non-parametric modeling

Oxygen uptake plays a crucial role in the evaluation of endurance performance during exercise and is extensively utilized for metabolic assessment. This study records the oxygen uptake during the exercise phase (i.e., ascending or descending) of the stair exercise, utilizing an experimental dataset that includes ten participants and covers various exercise periods. Based on the designed experiment protocol, a non-parametric modeling method with kernel-based regularization is generally applied to estimate the oxygen uptake changes during the switching stairs exercise, which closely resembles daily life activities. The modeling results indicate the effectiveness of the non-parametric modeling approach when compared to fixed-order models in terms of accuracy, stability, and compatibility. The influence of exercise duration on estimated fitness reveals that the model of the phase-oxygen uptake system is not time-invariant related to respiratory metabolism regulation and muscle fatigue. Consequently, it allows us to study the humans’ conversion mechanism at different metabolic rates and facilitates the standardization and development of exercise prescriptions.

Rural-urban Migration and Dynamics of Income Distribution in China:A Non-parametric Approach

Extending the income dynamics approach in Quah （2003）, the present paper studies the enlarging income inequality in China over the past three decades from the viewpoint of rural-urban migration and economic transition. We establish non-parametric estimations of rural and urban income distribution functions in China, and aggregate a population- weighted, nationwide income distribution function taking into account rural-urban differences in technological progress and price indexes. We calculate 12 inequality indexes through non-parametric estimation to overcome the biases in existingparametric estimation and, therefore, provide more accurate measurement of income inequalitY. Policy implications have been drawn based on our research.

Incorporating travel time reliability in predicting the likelihood of severe crashes on arterial highways using non-parametric random-effect regression

Travel time reliability(TTR) modeling has gain attention among researchers’ due to its ability to represent road user satisfaction as well as providing a predictability of a trip travel time.Despite this significant effort,its impact on the severity of a crash is not well explored.This study analyzes the effect of TTR and other variables on the probability of the crash severity occurring on arterial roads.To address the unobserved heterogeneity problem,two random-effect regressions were applied;the Dirichlet random-effect(DRE)and the traditional random-effect(TRE) logistic regression.The difference between the two models is that the random-effect in the DRE is non-parametrically specified while in the TRE model is parametrically specified.The Markov Chain Monte Carlo simulations were adopted to infer the parameters’ posterior distributions of the two developed models.Using four-year police-reported crash data and travel speeds from Northeast Florida,the analysis of goodness-of-fit found the DRE model to best fit the data.Hence,it was used in studying the influence of TTR and other variables on crash severity.The DRE model findings suggest that TTR is statistically significant,at 95 percent credible intervals,influencing the severity level of a crash.A unit increases in TTR reduces the likelihood of a severe crash occurrence by 25 percent.Moreover,among the significant variables,alcohol/drug impairment was found to have the highest impact in influencing the occurrence of severe crashes.Other significant factors included traffic volume,weekends,speed,work-zone,land use,visibility,seatbelt usage,segment length,undivided/divided highway,and age.

Seismic fragility curves for structures using non-parametric representations

Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion （e.g., the maximal inter-storey drift of a building exceeding a certain threshold） is represented as a function of the intensity of the earthquake ground motion （e.g., peak ground acceleration or spectral acceleration）. The classical approach relies on assuming a lognormal shape of the fragility curves; it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random,and establish the asymptotic normality of these estimators.As their applications,we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function,the conditional density function and the conditional quantile function,and investigate the asymptotic normality of these estimators.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators.

Variable selection in identification of a high dimensional nonlinear non-parametric system

The problem of variable selection in system identification of a high dimensional nonlinear non-parametric system is described. The inherent difficulty, the curse of dimensionality, is introduced. Then its connections to various topics and research areas are briefly discussed, including order determination, pattern recognition, data mining, machine learning, statistical regression and manifold embedding. Finally, some results of variable selection in system identification in the recent literature are presented.

Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.

Evaluation of Rainfall Tendency for the Twentieth Century over Indira Sagar Region in Central India

The study investigates long-term changes in annual and seasonal rainfall patterns in the Indira Sagar Region of Madhya Pradesh, India, from 1901 to 2010. Agriculture sustainability, food supply, natural resource development, and hydropower system reliability in the region rely heavily on monsoon rainfall. Monthly rainfall data from three stations (East Nimar, Barwani, and West Nimar) were analyzed. Initially, the pre-whitening method was applied to eliminate serial correlation effects from the rainfall data series. Subsequently, statistical trends in annual and seasonal rainfall were assessed using both parametric (student-t test) and non-parametric tests [Mann-Kendall, Sen’s slope estimator, and Cumulative Sum (CUSUM)]. The magnitude of the rainfall trend was determined using Theil-Sen’s slope estimator. Spatial analysis of the Mann-Kendall test on an annual basis revealed a statistically insignificant decreasing trend for Barwani and East Nimar and an increasing trend for West Nimar. On a seasonal basis, the monsoon season contributes a significant percentage (88.33%) to the total annual rainfall. The CUSUM test results indicated a shift change detection in annual rainfall data for Barwani in 1997, while shifts were observed in West and East Nimar stations in 1929. These findings offer valuable insights into regional rainfall behavior, aiding in the planning and management of water resources and ecological systems.

Parameters Estimation of a Bivariate Generalized Poisson Distribution with Applications to Metabolic Syndrome Data

Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.

Recovering implied risk-neutral probability density function using SVR

Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.

AN OPERATIONAL STATISTICAL SCHEME FOR TROPICAL CYCLONE INDUCED RAINFALL FORECAST

A non-parametric method is used in this study to analyze and predict short-term rainfall due to tropical cyclones(TCs) in a coastal meteorological station. All 427 TCs during 1953-2011 which made landfall along the Southeast China coast with a distance less than 700 km to a certain meteorological station- Shenzhen are analyzed and grouped according to their landfalling direction, distance and intensity. The corresponding daily rainfall records at Shenzhen Meteorological Station(SMS) during TCs landfalling period(a couple of days before and after TC landfall) are collected. The maximum daily rainfall(R-24) and maximum 3-day accumulative rainfall(R-72) records at SMS for each TC category are analyzed by a non-parametric statistical method, percentile estimation. The results are plotted by statistical boxplots, expressing in probability of precipitation. The performance of the statistical boxplots is evaluated to forecast the short-term rainfall at SMS during the TC seasons in 2012 and 2013. Results show that the boxplot scheme can be used as a valuable reference to predict the short-term rainfall at SMS due to TCs landfalling along the Southeast China coast.