Nonparametric Statistical Feature Scaling Based Quadratic Regressive Convolution Deep Neural Network for Software Fault Prediction

The development of defect prediction plays a significant role in improving software quality. Such predictions are used to identify defective modules before the testing and to minimize the time and cost. The software with defects negatively impacts operational costs and finally affects customer satisfaction. Numerous approaches exist to predict software defects. However, the timely and accurate software bugs are the major challenging issues. To improve the timely and accurate software defect prediction, a novel technique called Nonparametric Statistical feature scaled QuAdratic regressive convolution Deep nEural Network (SQADEN) is introduced. The proposed SQADEN technique mainly includes two major processes namely metric or feature selection and classification. First, the SQADEN uses the nonparametric statistical Torgerson–Gower scaling technique for identifying the relevant software metrics by measuring the similarity using the dice coefficient. The feature selection process is used to minimize the time complexity of software fault prediction. With the selected metrics, software fault perdition with the help of the Quadratic Censored regressive convolution deep neural network-based classification. The deep learning classifier analyzes the training and testing samples using the contingency correlation coefficient. The softstep activation function is used to provide the final fault prediction results. To minimize the error, the Nelder–Mead method is applied to solve non-linear least-squares problems. Finally, accurate classification results with a minimum error are obtained at the output layer. Experimental evaluation is carried out with different quantitative metrics such as accuracy, precision, recall, F-measure, and time complexity. The analyzed results demonstrate the superior performance of our proposed SQADEN technique with maximum accuracy, sensitivity and specificity by 3%, 3%, 2% and 3% and minimum time and space by 13% and 15% when compared with the two state-of-the-art methods.

Nonparametric Estimation of the Trend Function for Stochastic Processes Driven by Fractional Brownian Motion of the Second Kind

The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.

Nonparametric Feature Screening via the Variance of the Regression Function

This article develops a procedure for screening variables, in ultra high-di- mensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their respective marginal regression functions (RV-SIS). We show that, under some mild technical conditions, the RV-SIS possesses a sure screening property, which is defined by Fan and Lv (2008). Numerical comparisons suggest that RV-SIS has competitive performance compared to other screening procedures, and outperforms them in many different model settings.

A nonparametric spectrum estimation method for dispersion and attenuation analysis of borehole acoustic measurements

Dispersion and attenuation analysis can be used to determine formation anisotropy induced by fractures,or stresses.In this paper,we propose a nonparametric spectrum estimation method to get phase dispersion characteristics and attenuation coefficient.By designing an appropriate vector filter,phase velocity,attenuation coefficient and amplitude can be inverted from the waveform recorded by the receiver array.Performance analysis of this algorithm is compared with Extended Prony Method(EPM)and Forward and Backward Matrix Pencil(FBMP)method.Based on the analysis results,the proposed method is capable of achieving high resolution and precision as the parametric spectrum estimation methods.At the meantime,it also keeps high stability as the other nonparametric spectrum estimation methods.At last,applications to synthetic waveforms modeled using finite difference method and real data show its efficiency.The real data processing results show that the P-wave attenuation log is more sensitive to oil formation compared to S-wave;and the S-wave attenuation log is more sensitive to shale formation compared to P-wave.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

Modulation classification of MPSK signals based on nonparametric Bayesian inference

A nonparametric Bayesian method is presented to classify the MPSK （M-ary phase shift keying） signals. The MPSK signals with unknown signal noise ratios （SNRs） are modeled as a Gaussian mixture model with unknown means and covariances in the constellation plane, and a clustering method is proposed to estimate the probability density of the MPSK signals. The method is based on the nonparametric Bayesian inference, which introduces the Dirichlet process as the prior probability of the mixture coefficient, and applies a normal inverse Wishart （NIW） distribution as the prior probability of the unknown mean and covariance. Then, according to the received signals, the parameters are adjusted by the Monte Carlo Markov chain （MCMC） random sampling algorithm. By iterations, the density estimation of the MPSK signals can be estimated. Simulation results show that the correct recognition ratio of 2/4/8PSK is greater than 95% under the condition that SNR 〉5 dB and 1 600 symbols are used in this method.

DIAGNOSTIC CHECKING FOR TIME SERIES MODELS USING NONPARAMETRIC APPROACH

In time series modeling, the residuals are often checked for white noise and normality. In practice, the useful tests are Ljung Box test. Mcleod Li test and Lin Mudholkar test. In this paper, we present a nonparametric approach for checking the residuals of time series models. This approach is based on the maximal correlation coefficient ρ 2 * between the residuals and time t . The basic idea is to use the bootstrap to form the null distribution of the statistic ρ 2 * under the null hypothesis H 0:ρ 2 * =0. For calculating ρ 2 * , we proposes a ρ algorithm, analogous to ACE procedure. Power study shows this approach is more powerful than Ljung Box test. Meanwhile, some numerical results and two examples are reported in this paper.

Nonparametric Control Scheme for Monitoring Phase Ⅱ Nonlinear Profiles with Varied Argument Values

Profile monitoring is used to check the stability of the quality of a product over time when the product quality is best represented by a function at each time point.However,most previous monitoring approaches have not considered that the argument values may vary from profile to profile,which is common in practice.A novel nonparametric control scheme based on profile error is proposed for monitoring nonlinear profiles with varied argument values.The proposed scheme uses the metrics of profile error as the statistics to construct the control charts.More details about the design of this nonparametric scheme are also discussed.The monitoring performance of the combined control scheme is compared with that of alternative nonparametric methods via simulation.Simulation studies show that the combined scheme is effective in detecting parameter error and is sensitive to small shifts in the process.In addition,due to the properties of the charting statistics,the out-of-control signal can provide diagnostic information for the users.Finally,the implementation steps of the proposed monitoring scheme are given and applied for monitoring the blade manufacturing process.With the application in blade manufacturing of aircraft engines,the proposed nonparametric control scheme is effective,interpretable,and easy to apply.

Strong Convergence of Partitioning Estimation for Nonparametric Regression Function under Dependence Samples

In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.

NONPARAMETRIC DETECTION OF RADAR TARGET IN NONHOMOGENEOUS ENVIRONMENTS

This poaper is devoted to the performance evaluation of the Generalized Sigu(GS). Trimmed Generalized Sign(TGS), Modified Savage(MS). Mann-Whitney(MW) and a new proposed detector in multiple target situations. The analysis is carried out for both fluctuating and nonfluctuating received signals. The simulation results show that the new proposed detector has the best detection performance in homogeneous as well as nonhomogeneous background conditions, while TGS procedure is better than the GS detector in distinguishing the primary target from the secondary interfering ones.

Using Evolutionary Computation to Solve Problems in Nonparametric Regression

This paper studies evolutionary mechanism of parameter selection in the construction of weight function for Nearest Neighbour Estimate in nonparametric regression. Construct an algorithm which adaptively evolves fine weight and makes good prediction about unknown points. The numerical experiments indicate that this method is effective. It is a meaningful discussion about practicability of nonparametric regression and methodology of adaptive model-building.

Nonparametric estimations of the sea state bias for a radar altimeter

To estimate the sea state bias（SSB） for radar altimeter, two nonparametric models, including a Nadaraya-Watson（NW） kernel estimator and a local linear regression（LLR） estimator, are studied based on the Jason-2 altimeter data. Selecting from different combinations of the Gaussian kernel function, spherical Epanechnikov kernel function, a fixed bandwidth and a local adjustable bandwidth, it is observed that the LLR method with the spherical Epanechnikov kernel function and the local adjustable bandwidth is the optimal nonparametric model for the SSB estimation. The comparisons between the nonparametric and parametric models are conducted and the results show that the nonparametric model performs relatively better at high-latitudes of the Northern Hemisphere. This method has been applied to the HY-2A altimeter as well and the same conclusion can be obtained.

BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES

This paper introduces a method of bootstrap wavelet estimation in a non-parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.

Floating Car Data Based Nonparametric Regression Model for Short-Term Travel Speed Prediction

A K-nearest neighbor （K-NN） based nonparametric regression model was proposed to predict travel speed for Beijing expressway. By using the historical traffic data collected from the detectors in Beijing expressways, a specically designed database was developed via the processes including data filtering, wavelet analysis and clustering. The relativity based weighted Euclidean distance was used as the distance metric to identify the K groups of nearest data series. Then, a K-NN nonparametric regression model was built to predict the average travel speeds up to 6 min into the future. Several randomly selected travel speed data series, collected from the floating car data （FCD） system, were used to validate the model. The results indicate that using the FCD, the model can predict average travel speeds with an accuracy of above 90%, and hence is feasible and effective.

Nonparametric TOA estimators for low-resolution IR-UWB digital receiver

Nonparametric time-of-arrival（TOA） estimators for impulse radio ultra-wideband（IR-UWB） signals are proposed. Nonparametric detection is obviously useful in situations where detailed information about the statistics of the noise is unavailable or not accurate. Such TOA estimators are obtained based on conditional statistical tests with only a symmetry distribution assumption on the noise probability density function. The nonparametric estimators are attractive choices for low-resolution IR-UWB digital receivers which can be implemented by fast comparators or high sampling rate low resolution analog-to-digital converters（ADCs）,in place of high sampling rate high resolution ADCs which may not be available in practice. Simulation results demonstrate that nonparametric TOA estimators provide more effective and robust performance than typical energy detection（ED） based estimators.

Nonparametric Identification of Nonlinear Added Mass Moment of Inertia and Damping Moment Characteristics of Large-Amplitude Ship Roll Motion

This study aims to investigate the nonlinear added mass moment of inertia and damping moment characteristics of largeamplitude ship roll motion based on transient motion data through the nonparametric system identification method.An inverse problem was formulated to solve the first-kind Volterra-type integral equation using sets of motion signal data.However,this numerical approach leads to solution instability due to noisy data.Regularization is a technique that can overcome the lack of stability;hence,Landweber’s regularization method was employed in this study.The L-curve criterion was used to select regularization parameters(number of iterations)that correspond to the accuracy of the inverse solution.The solution of this method is a discrete moment,which is the summation of nonlinear restoring,nonlinear damping,and nonlinear mass moment of inertia.A zero-crossing detection technique is used in the nonparametric system identification method on a pair of measured data of the angular velocity and angular acceleration of a ship,and the detections are matched with the inverse solution at the same discrete times.The procedure was demonstrated through a numerical model of a full nonlinear free-roll motion system in still water to examine and prove its accuracy.Results show that the method effectively and efficiently identified the functional form of the nonlinear added moment of inertia and damping moment.

NONPARAMETRIC POLYSPECTRAL ESTIMATORS FOR k-TH-ORDER (ALMOST) CYCLOSTATIONARY COMPLEX PROCESSES

Higher-order almost cyclostationary complex processes are complex random signals with almost periodically time-varying statistics, which is important to the research of non-Gaussian signals in information system. In tins paper, smoothed polyperiodograms are proposed for related to cyclic polyspectral estimation and are shown to be consistent and asymptotically complex normal. Asymptotic covariance expressions are derived along with their computable forms.

Nonparametric estimation for hazard rate monotonously decreasing system

Estimation of density and hazard rate is very important to the reliability analysis of a system. In order to estimate the density and hazard rate of a hazard rate monotonously decreasing system, a new nonparametric estimator is put forward. The estimator is based on the kernel function method and optimum algorithm. Numerical experiment shows that the method is accurate enough and can be used in many cases.

Testing heteroscedasticity in nonparametric regression models based on residual analysis

The importance of detecting heteroscedasticity in regression analysis is widely recognized because efficient inference for the regression function requires that heteroscedasticity should be taken into account. In this paper, a simple test for heteroscedasticity is proposed in nonparametric regression based on residual analysis. Furthermore, some simulations with a comparison with Dette and Munk＇s method are conducted to evaluate the performance of the proposed test. The results demonstrate that the method in this paper performs quite satisfactorily and is much more powerful than Dette and Munk＇s method in some cases.