A novel nonparametric computational strategy for identifying differential methylation regions

Background DNA methylation has long been known as an epigenetic gene silencing mechanism. For a motivating example, the methylomes of cancer and non-cancer cells show a number of methylation differences, indicating that certain features characteristics of cancer cells may be related to methylation characteristics. Robust methods for detecting differentially methylated regions (DMRs) could help scientists narrow down genome regions and even find biologically important regions. Although some statistical methods were developed for detecting DMR, there is no default or strongest method. Fisher’s exact test is direct, but not suitable for data with multiple replications, while regression-based methods usually come with a large number of assumptions. More complicated methods have been proposed, but those methods are often difficult to interpret. Results In this paper, we propose a three-step nonparametric kernel smoothing method that is both flexible and straightforward to implement and interpret. The proposed method relies on local quadratic fitting to find the set of equilibrium points (points at which the first derivative is 0) and the corresponding set of confidence windows. Potential regions are further refined using biological criteria, and finally selected based on a Bonferroni adjusted t-test cutoff. Using a comparison of three senescent and three proliferating cell lines to illustrate our method, we were able to identify a total of 1077 DMRs on chromosome 21. Conclusions We proposed a completely nonparametric, statistically straightforward, and interpretable method for detecting differentially methylated regions. Compared with existing methods, the non-reliance on model assumptions and the straightforward nature of our method makes it one competitive alternative to the existing statistical methods for defining DMRs.

NONPARAMETRIC KERNEL DISTRIBUTION FUNCTION ESTIMATION NEAR ENDPOINTS

In this paper, two kernel cumulative distribution function estimators are introduced and investigated in order to improve the boundary effects, we will restrict our attention to the right boundary. The first estimator uses a self-elimination between modify theoretical Bias term and the classical kernel estimator itself. The basic technique of construction the second estimator is kind of a generalized reflection method involving reflection a transformation of the observed data. The theoretical properties of our estimators turned out that the Bias has been reduced to the second power of the bandwidth, simulation studies and two real data applications were carried out to check these phenomena and are conducted that the proposed estimators are better than the existing boundary correction methods.

A Comparison Between New Modification of ANWK and Classical ANWK Methods in Nonparametric Regression

Nonparametric kernel estimators are mostly used in a variety of statistical research fields. Nadaraya-Watson kernel estimator (NWK) is one of the most important nonparametric kernel estimator that is often used in regression models with a fixed bandwidth. In this article, we consider the four new Proposed Adaptive Nadaraya-Watson Kernel Regression Estimators (Interquartile Range, Standard Deviation, Mean Absolute Devotion, and Median Absolute Deviation) rather than (Fixed Bandwidth, Adaptive Geometric, Adaptive Mean, Adaptive Range, and Adaptive Median). The outcomes in both simulation and actual data in Leukemia Cancer show that the four new ANW Kernel Estimators (Interquartile Range, Standard Deviation, Mean Absolute devotion, and Median Absolute Deviation) is more effective than the kernel estimations with fixed bandwidth in previous studies using Mean Square Error (MSE) Criterion.

Can Machine Learning be Applied to Carbon Emissions Analysis: An Application to the CO2 Emissions Analysis Using Gaussian Process Regression

In this paper, a nonparametric kernel prediction algorithm in machine learning is applied to predict CO2 emissions. A literature review has been conducted so that proper independent variables can be identified. Traditional parametric modeling approaches and the Gaussian Process Regression (GPR) algorithms were introduced, and their prediction performance was summarized. The reliability and efficiency of the proposed algorithms were then demonstrated through the comparison of the actual and the predicted results. The results showed that the GPR method can give the most accurate predictions on CO2 emissions.

The Novel Successive Variational Mode Decomposition and Weighted Regularized Extreme Learning Machine for Fault Diagnosis of Automobile Gearbox

In order to improve the diagnosis accuracies of the current diagnosis methods, a novel fault diagnosis method of automobile gearbox based on novel successive variational mode decomposition and weighted regularized extreme learning machine is presented for fault diagnosis of gearbox in this paper. The novel successive variational mode decomposition (SVMD) is presented to improve the traditional variational mode decomposition, which finds modes one after the other, and this succession helps increase convergence rate and also not extract the unwanted modes; weighted regularized extreme learning machine (WRELM) is presented to improve the traditional extreme learning machine, which uses the weight of each sample with the nonparametric kernel density estimation and can find the optimal weight for each sample. The test results indicate that the diagnosis accuracy of SVMD-WRELM for gearbox is better than that of VMD-WRELM, VMD-ELM.

ESTIMATION OF TIME-VARYING COVARIANCE MATRICES FOR LARGE DATASETS

Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently, there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or nonparametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible dependence and heavy-tailed distributions. In this paper, we introduce a nonparametric version of regularization techniques for sparse large covariance matrices, developed by Bickel and Levina (2008) and others. We focus on the robustness of such a procedure to time variation, dependence and heavy-tailedness of distributions. The paper includes a set of results on Bernstein type inequalities for dependent unbounded variables which are expected to be applicable in econometric analysis beyond estimation of large covariance matrices. We discuss the utility of the robust thresholding method, comparing it with other estimators in simulations and an empirical application on the design of minimum variance portfolios.

Reliability Analysis of Photovoltaic charging Station of Electric vehicle considering the relationship between Photovoltaic output and charging load

The intermittency and randomicity of photovoltaic output will have a great influence on the reliability of photovoltaic charging station. Based on the photovoltaic output and charging load data of a photovoltaic charging station in our country, the reliability of photovoltaic charging station is evaluated. Firstly, the probability distributions of photovoltaic output and charging load are calculated respectively by using nonparametric kernel density estimation method. Secondly, the Copula function is optimized according to the correlation degree. Finally, a hybrid Copula function is constructed to describe the correlation between PV output and EV charging load, and an example is given to verify the reliability of the PV charging station.