Optimal Smoothing Parameter Research Articles

Comparisons of some new and existing EWMA schemes for binomial count processes with applications to monitoring hospital No-Shows

ABSTRACT Applications of several exponentially weighted moving average (EWMA) schemes for monitoring binomial count data have been widely used in the manufacturing and healthcare industries. However, practitioners may be confused about selecting the appropriate scheme for their needs. In this paper, we compare the performance of some existing EWMA schemes and a new EWMA scheme utilizing the weighted likelihood ratio test (WLRT), referred to as the EWLRT scheme. Firstly, some properties of the EWLRT scheme for binomial proportion are outlined. Next, a method for choosing the optimal smoothing parameter based on the relative mean index (RMI) is described, and various competing schemes are compared at the optimal level, which was not done in most previous studies. Additionally, current comparisons consider the zero-state (ZS) run-length performance and the conditional expected delay (CED) for a delayed shift. The results based on the Monte Carlo method indicate that the EWLRT scheme’s efficacy is somewhat more encouraging than that of its competitors in detecting small to moderate changes in terms of CED. Finally, a real example of monitoring hospital No-Shows, a necessary healthcare management process, describes the implementation.

Dynamic pricing strategies for efficient inventory management with auto-correlative stochastic demand forecasting using exponential smoothing method

The research presents a novel approach to inventory modelling, emphasizing stochastic demand and dynamic pricing strategies for a seasonal sales framework. The methodology divides the sales season into intervals, each associated with distinct pricing strategies influenced by stochastic factors. The study employ exponential smoothing for demand forecasting, optimizing inventory replenishment and dynamic pricing strategies through developed algorithms. Notably, the study determine the optimal smoothing parameter for demand forecasting, balancing responsiveness to recent demand patterns with long-term stability. Proposed research achieves a comprehensive framework empowering businesses to enhance competitiveness and profitability by addressing challenges of stochastic demand and dynamic pricing. Dynamic pricing strategies outperformed classical strategies, allowing businesses to respond promptly to demand fluctuations and optimize profit margins during sales seasons. Incorporating stochastic demand models enabled organizations to implement safety stock and buffer inventory levels effectively, mitigating risks associated with uncertain demand patterns. Real-time data analysis was crucial for adjusting price dynamics and making effective management decisions, leading to improved financial performance. The iterative nature of dynamic pricing strategies emphasized the importance of continuous refinement to adapt to evolving market dynamics. This approach enables data-driven decisions, adaptation to market fluctuations, and improved inventory management despite unpredictable demand. Ultimately, this study provides valuable insights and methodologies applicable across industries for efficient and profitable inventory management.

Assessment of computing systems reliability by non-parametric method by small samples of operational data

A new method for assessing the reliability of small computing systems that allows the generation of only small samples of operational data is proposed in the article. The result of applying the technique is the posterior failure distribution density, on the basis of which various reliability indicators can be calculated. The methodology consists of two stages: the first is the preparation of operational data, including detection of failures using machine learning methods, and the second is the construction of the failure distribution density using the adapted Rosenblatt–Parzen method. Increasing the efficiency of estimates using the proposed method is achieved by taking into account censored data, compensating for the shift of failure distribution densities and finding the optimal smoothing parameter.

A reliable data-based smoothing parameter selection method for circular kernel estimation

A new data-based smoothing parameter for circular kernel density (and its derivatives) estimation is proposed. Following the plug-in ideas, unknown quantities on an optimal smoothing parameter are replaced by suitable estimates. This paper provides a circular version of the well-known Sheather and Jones bandwidths (J R Stat Soc Ser B Stat Methodol 53(3):683–690, 1991. https://doi.org/10.1111/j.2517-6161.1991.tb01857.x), with direct and solve-the-equation plug-in rules. Theoretical support for our developments, related to the asymptotic mean squared error of the estimator of the density, its derivatives, and its functionals, for circular data, are provided. The proposed selectors are compared with previous data-based smoothing parameters for circular kernel density estimation. This paper also contributes to the study of the optimal kernel for circular data. An illustration of the proposed plug-in rules is also shown using real data on the time of car accidents.

Construction of a Questionnaire System for College Students’ Consumption Views Based on Discrete Regression Algorithm in the Context of Ideological and Political Education

Abstract This paper constructs a questionnaire system for college students’ consumption views based on the discrete regression algorithm combined with the questionnaire method. The least squares staggered identification method is employed in the discrete regression algorithm to select the window width and reduce the integral square error of the estimation. On the basis of continuous and discrete data, the density function and regression function are estimated, and the parametric and nonparametric estimation methods are utilized to select the optimal smoothing parameters of the regression function by the method of least squares interleaved identification. In the survey of college students’ consumption outlook, the consumption outlook of college students in colleges and universities in the S province region is taken as the research object. In the questionnaire analysis, it is known that the first factor considered by college students is the sustainable use of products. The mean value of the sustainability dimension is 4.86, and the last factor considered is the ostentatiousness and extravagance of the consumption products, and the mean values are 2.65 and 2.71, respectively. Each basic situation of the college students and the social, family, personal, and influencing factors have a significant predictive effect on each dimension of the college students’ consumption outlook status.

Optimal Smoothing of the Wind–Wave Spectrum Based on the Confidence-Interval Trade-Off

In this study, a smoothing method was applied to improve the accuracy of peak wave period estimation using water surface elevation data collected from two oceanographic and meteorological observation towers situated on the western coast of the Korean Peninsula. The effectiveness of the smoothing method was validated by assessing the surface elevation variance and total wave energy. Subsequently, we examined the impact of the smoothing application. The results of our analysis revealed a reduction of approximately 27% in comparison to the confidence interval of the initially estimated spectrum upon applying the smoothing method. Furthermore, a slight variation of approximately 1–2 s was observed between the peak wave period calculated from the estimated spectrum and that obtained through the smoothing process. Utilizing statistical methods to determine the optimal smoothing parameter count, we observed an increasing trend as the range of significant wave heights decreased.

Forecasting the Indonesian Coffee Production and Consumption Using the Modified Golden Section Search to Estimate the Smoothing Parameters

The Double Exponential Smoothing (DES) and Triple Exponential Smoothing (TES) are forecasting methods that require two and three smoothing parameters, respectively. Smoothing parameters are often determined through a trial and error process that is not really efficient since many experiments need to be done. Therefore, in this study, a smoothing parameter estimation algorithm is conducted in the form of the modified Golden Section Search (GSS) to obtain the optimal smoothing parameters from the DES and TES methods. Forecasting is carried out on production, domestic consumption, and export consumption data of Indonesian coffee, which is one of the leading agricultural sub-sector commodities. The data is obtained from the Ministry of Agriculture of the Republic of Indonesia. The smoothing parameters obtained by applying the modified GSS are used to forecast production and domestic consumption data using the DES method, while the forecasting of the export consumption data is done with the TES method. All of the MAPE values are less than 20% which indicates that the smoothing parameters obtained by using the modified GSS are able to perform good forecasting. The results show that coffee production in Indonesia cannot meet its demand until 2024 since the total coffee consumption exceeds the production.

Forecasting the Indonesian Coffee Production and Consumption Using the Modified Golden Section Search to Estimate the Smoothing Parameters

The Double Exponential Smoothing (DES) and Triple Exponential Smoothing (TES) are forecasting methods that require two and three smoothing parameters, respectively. Smoothing parameters are often determined through a trial and error process that is not really efficient since many experiments need to be done. Therefore, in this study, a smoothing parameter estimation algorithm is conducted in the form of the modified Golden Section Search (GSS) to obtain the optimal smoothing parameters from the DES and TES methods. Forecasting is carried out on production, domestic consumption, and export consumption data of Indonesian coffee, which is one of the leading agricultural sub-sector commodities. The data is obtained from the Ministry of Agriculture of the Republic of Indonesia. The smoothing parameters obtained by applying the modified GSS are used to forecast production and domestic consumption data using the DES method, while the forecasting of the export consumption data is done with the TES method. All of the MAPE values are less than 20% which indicates that the smoothing parameters obtained by using the modified GSS are able to perform good forecasting. The results show that coffee production in Indonesia cannot meet its demand until 2024 since the total coffee consumption exceeds the production.

Percentile Bootstrap Interval on Univariate Local Polynomial Regression Prediction

This study offers a new technique for constructing percentile bootstrap intervals to predict the regression of univariate local polynomials. Bootstrap regression uses resampling derived from paired and residual bootstrap methods. The main objective of this study is to perform a comparative analysis between the two resampling methods by considering the nominal coverage probability. Resampling uses a nonparametric bootstrap technique with the return method, where each sample point has an equal chance of being selected. The principle of nonparametric bootstrapping uses the original sample data as a source of diversity in contrast to parametric bootstrapping, where the variety comes from generating a particular distribution. The simulation results show that the paired and residual bootstrap interval coverage probabilities are close to nominal coverage. The results showed no significant difference between paired bootstrap interval and percentile residual. Increasing the bootstrap sample size sufficiently large gives the scatterplot smoothness of the confidence interval. Applying the smoothing parameter by choice gives a second-order polynomial regression with a smoother distribution than the first-order polynomial regression. The scatterplot shows that the second-degree polynomial regression can capture the data curvature feature compared to the first-degree polynomial. The bands made from second-degree polynomials give a narrower width than first-degree polynomials. In contrast, applying optimal smoothing parameters to the model provides different conclusions by using smoothing parameters based on choice. In addition to the differences based on the scatterplot, the bootstrap estimates of the coverage probability are also other. Selecting smoothing parameters based on a particular value provides probability coverage with the paired bootstrap method for the first-degree local polynomial regression is 0.93, while the second-degree local polynomial is 0.96. The probability of coverage based on the residual bootstrap method for the first-degree local polynomial regression is 0.95, while the second-degree local polynomial is 0.96. The probability coverage based on the optimal parameters of the paired bootstrap method for the first-degree local polynomial regression is 0.945, while the second-degree local polynomial is 0.93. The residual bootstrap method gives the first-degree local polynomial regression of 0.95, while the second-degree local polynomial is 0.93. In general, both bootstrap methods work well for estimating prediction confidence intervals.

Compensation-Based Output Feedback Control for Fuzzy Markov Jump Systems With Random Packet Losses.

This article is concerned with the problem of compensation-based output feedback control for Takagi-Sugeno fuzzy Markov jump systems subject to packet losses. The phenomenon of packet losses is assumed to randomly occur in the feedback channel, which is modeled by a Bernoulli process. Employing the single exponential smoothing method as a compensation scheme, the missing measurements are predicted to help offset the impact of packet losses on system performance. Then, an asynchronous output feedback controller is designed by the hidden Markov model. Based on the mode-dependent Lyapunov function, some novel sufficient conditions on the controller existence are derived such that the closed-loop system is stochastically stable with strict dissipativity. Besides, an algorithm for determining the optimal smoothing parameter is proposed. Finally, the validity and advantages of the design approach are manifested by some simulation results.

Bootstrap-t Confidence Interval on Local Polynomial Regression Prediction

In local polynomial regression, prediction confidence interval estimation using standard theory will give coverage probability close to exact coverage probability. However, if the normality assumption is not met, the bootstrap method makes it possible to apply it. The working principle of the bootstrap method uses the resampling method where the sample data becomes a population and there is no need to know the distribution of the sample data is normal or not. Indiscriminate selection of smoothing parameters allows scatterplot results from local polynomial regressions to be rough and can even lead to misleading statistical conclusions. It is necessary to consider the optimal smoothing parameters to get local polynomial regression predictions that are not overfitting or underfitting. We offer two new algorithms based on the nested bootstrap resampling method to determine the bootstrap-t confidence interval in predicting local polynomial regression. Both algorithms consider the search for optimal smoothing parameters. The first algorithm performs paired and residual bootstrap samples, and the second algorithm performs based on residuals with residuals. The first algorithm provides a scatterplot and reasonable coverage probability on relatively large sample data. In contrast, the second algorithm is more powerful for each data size, including for relatively small sample data sizes. The mean of the bootstrap-t confidence interval coverage probability shows that the second algorithm for second-degree local polynomial regression is better than the other three. However, the larger the sample data size gives, the closer the closer the average coverage probability of the two algorithms is to the nominal coverage probability.

Reproducing Kernel Hilbert Space Approach to Multiresponse Smoothing Spline Regression Function

In statistical analyses, especially those using a multiresponse regression model approach, a mathematical model that describes a functional relationship between more than one response variables and one or more predictor variables is often involved. The relationship between these variables is expressed by a regression function. In the multiresponse nonparametric regression (MNR) model that is part of the multiresponse regression model, estimating the regression function becomes the main problem, as there is a correlation between the responses such that it is necessary to include a symmetric weight matrix into a penalized weighted least square (PWLS) optimization during the estimation process. This is, of course, very complicated mathematically. In this study, to estimate the regression function of the MNR model, we developed a PWLS optimization method for the MNR model proposed by a previous researcher, and used a reproducing kernel Hilbert space (RKHS) approach based on a smoothing spline to obtain the solution to the developed PWLS optimization. Additionally, we determined the symmetric weight matrix and optimal smoothing parameter, and investigated the consistency of the regression function estimator. We provide an illustration of the effects of the smoothing parameters for the estimation results using simulation data. In the future, the theory generated from this study can be developed within the scope of statistical inference, especially for the purpose of testing hypotheses involving multiresponse nonparametric regression models and multiresponse semiparametric regression models, and can be used to estimate the nonparametric component of a multiresponse semiparametric regression model used to model Indonesian toddlers’ standard growth charts.

Dynamic light scattering inversion based on Tikhonov regularization and parameter-optimized generalized regression neural network

Neural network technology shows certain superiority in the field of dynamic light scattering (DLS) inversion. However, due to the complex problems of training sample and parameter selection, its application has certain limitations. At present, it has not been applied to the inversion of bimodal particle size distribution (PSD). Aiming at training sample generation and smoothing parameter optimization of generalized regression neural network (GRNN), a DLS inversion method combining Tikhonov regularization and parameter-optimized GRNN (Tikhonov-PGRNN) is proposed. In this method, the PSD of Tikhonov regularization inversion is used as prior information to generate the training samples, the one-dimensional search method is used to obtain the optimal smoothing parameter, and the normalized field autocorrelation function data is input into GRNN to estimate the PSD. Simulated data for narrow and broad 522 nm unimodal, 216 nm/667 nm bimodal PSDs were inverted by Tikhonov-PGRNN and Tikhonov under different noise levels. The results show that Tikhonov-PGRNN can realize the inversion of unimodal and bimodal PSDs. Compared with Tikhonov, the peak position error and the distribution error of PSDs inverted by Tikhonov-PGRNN are smaller and the method has higher anti-noise performance. The inversion results of experimental data are consistent with the conclusion of simulation data. The peak position errors of 203 nm, 555 nm unimodal and 33 nm/203 nm, 306 nm/974 nm bimodal particle systems inverted by Tikhonov-PGRNN are 1.48%, 0.39% and 3.55%/0.76%, 7.90%/1.74% respectively, which are better than the inversion results of Tikhonov. • A DLS inversion method of Tikhonov-PGRNN is proposed. • Tikhonov inversion result is used as prior information to generate training samples. • Optimal smoothing parameter is obtained by one-dimensional search method. • Tikhonov-PGRNN has higher anti-noise performance. • Tikhonov-PGRNN can obtain a high-accuracy inversion result.

Multi-objective optimization of injection molded parts with insert based on IFOA-GRNN-NSGA-II

Abstract The physical properties of plastic products, such as local strength, wear resistance and electrical properties, can be improved by adding embedded parts in the appropriate position of the products, and the precision of plastic parts can also be improved. However, due to the addition of inserts, the flow and shrinkage around inserts will be affected. Compared with traditional injection molding products, the quality is difficult to predict. To solve this problem, the injection molded parts with inserts (electrostatic test box) was used as an example, according to the product structure, three objectives of volume shrinkage, warpage in the X direction, and warpage in the Z direction were optimized. A generalized regression neural network (GRNN) model was established with molding parameters as input and quality objectives as output. Improved fruit fly optimization algorithm (IFOA) was proposed to select the optimal smoothing parameters dynamically. Through the prediction of samples, the experimental results show that the model is superior to two comparative models. Non-dominated sorting genetic algorithm (NSGA-II) was used to solve the model, and the Pareto-optimal front was obtained. The entropy TOPSIS method was used to evaluate the Pareto-optimal front, and the optimal solution was obtained. The results show that IFOA-GRNN-NSGA is a reliable multi-objective optimization method.

Recognition of Upper Limb Action Intention Based on IMU.

Using motion information of the upper limb to control the prosthetic hand has become a hotspot of current research. The operation of the prosthetic hand must also be coordinated with the user’s intention. Therefore, identifying action intention of the upper limb based on motion information of the upper limb is key to controlling the prosthetic hand. Since a wearable inertial sensor bears the advantages of small size, low cost, and little external environment interference, we employ an inertial sensor to collect angle and angular velocity data during movement of the upper limb. Aiming at the action classification for putting on socks, putting on shoes and tying shoelaces, this paper proposes a recognition model based on the Dynamic Time Warping (DTW) algorithm of the motion unit. Based on whether the upper limb is moving, the complete motion data are divided into several motion units. Considering the delay associated with controlling the prosthetic hand, this paper only performs feature extraction on the first motion unit and the second motion unit, and recognizes action on different classifiers. The experimental results reveal that the DTW algorithm based on motion unit bears a higher recognition rate and lower running time. The recognition rate reaches as high as 99.46%, and the average running time measures 8.027 ms. In order to enable the prosthetic hand to understand the grasping intention of the upper limb, this paper proposes a Generalized Regression Neural Network (GRNN) model based on 10-fold cross-validation. The motion state of the upper limb is subdivided, and the static state is used as the sign of controlling the prosthetic hand. This paper applies a 10-fold cross-validation method to train the neural network model to find the optimal smoothing parameter. In addition, the recognition performance of different neural networks is compared. The experimental results show that the GRNN model based on 10-fold cross-validation exhibits a high accuracy rate, capable of reaching 98.28%. Finally, the two algorithms proposed in this paper are implemented in an experiment of using the prosthetic hand to reproduce an action, and the feasibility and practicability of the algorithm are verified by experiment.

Gaussian Filter for Brain SPECT Imaging

Background. The presence of a noise component on 3D images of single-photon emission computed tomo­graphy (SPECT) of a brain significantly distorts the probability distribution function (PD) of the radioactive count rate in the images. The presence of noise and further filtering of the data, based on a subjective assessment of image quality, have a significant impact on the calculation of volumetric cerebral blood flow and the values of the uptake asymmetry of the radiopharmaceutical in a brain. Objective. We are aimed to develop a method for optimal SPECT filtering of brain images with lipophilic radiopharmaceuticals, based on a Gaussian filter (GF), for subsequent image segmentation by the threshold method. Methods. SPECT images of the water phantom and the brain of patients with 99mTc-HMPAO were used. We have developed a technique for artificial addition of speckle noise to conditionally flawless data in order to determine the optimal parameters for smoothing SPECT, based on a GF. The quantitative criterion for optimal smoothing was the standard deviation between the PD of radioactive count rate of the smoothed image and conditionally ideal one. Results. It was shown that the maximum radioactive count rate of the SPECT image has an extremum by changing the standard deviation of the GF in the range of 0.3–0.4 pixels. The greater the noise component in the SPECT image, the more quasi-linearly the corresponding rate changes. This dependence allows determining the optimal smoothing parameters. The application of the developed smoothing technique allows restoring the probability distribution function of the radioactive count rate (distribution histogram) with an accuracy up to 5–10%. This provides the possibility to standardize SPECT images of brain. Conclusions. The research results of work solve a specific applied problem: restoration of the histogram of a radiopharmaceuticals distribution in a brain for correct quantitative assessment of regional cerebral blood flow. In contrast to the well-known publications on the filtration of SPECT data, the work takes into account that the initial tomographic data are 3D, rather than 2D slices, and contain not only uniform random Gaussian noise, but also a pronounced speckle component.

Heat transient processes identification of the elements of internal environment system

Introduction. The study of heat exchange transients in the climate system “Heater-Ventilator-Room”, when ventilator capacity varies step-wise, is presented. The construction of functional relations between inputs and outputs of the system is the object of special attention. This allows for a non-parametric identification of impulse responses in the system for simulation and control. Materials and methods. The climate system is represented by a combination of several different-type elements with step inputs and experimental data as outputs. Mathematical models of the elements are governed by Volterra integral equation of the 2nd kind. Solution of this equation is an ill-posed problem, and specifics of identification experiments do not allow applying computational methods of classical regularization algorithms. A non-parametric identification of impulse responses for the elements is performed by the authors’ stable algorithm with due regard for real technical systems specifics. The algorithm is founded on stable differentiation by smoothing cubic splines with optimal smoothing parameter estimation and special type boundary conditions. Results. Non-parametric identification algorithm is adapted for the investigated climate system. The inverse problems of impulse responses identification and the direct problems of heat flux reactions prediction are solved. A high convergence of theoretical and experimental data is shown. Conclusions. The behavior of the transients is predictable for the climate system under the particular operation mode. The algorithm proposed takes proper account of practical problems specifics. The results obtained suggest the efficiency of the algorithm for applied identification problems solutions in real complex technical systems.

Semi and Nonparametric Conditional Probability Density, a Case Study of Pedestrian Crashes

Background: Kernel-based methods have gained popularity as employed model residual’s distribution might not be defined by any classical parametric distribution. Kernel-based method has been extended to estimate conditional densities instead of conditional distributions when data incorporate both discrete and continuous attributes. The method often has been based on smoothing parameters to use optimal values for various attributes. Thus, in case of an explanatory variable being independent of the dependent variable, that attribute would be dropped in the nonparametric method by assigning a large smoothing parameter, giving them uniform distributions so their variances to the model’s variance would be minimal. Objectives: The objective of this study was to identify factors to the severity of pedestrian crashes based on an unbiased method. Especially, this study was conducted to evaluate the applicability of kernel-based techniques of semi- and nonparametric methods on the crash dataset by means of confusion techniques. Methods: In this study, two non- and semi-parametric kernel-based methods were implemented to model the severity of pedestrian crashes. The estimation of the semi-parametric densities is based on the adoptive local smoothing and maximization of the quasi-likelihood function, which is similar somehow to the likelihood of the binary logit model. On the other hand, the nonparametric method is based on the selection of optimal smoothing parameters in estimation of the conditional probability density function to minimize mean integrated squared error (MISE). The performances of those models are evaluated by their prediction power. To have a benchmark for comparison, the standard logistic regression was also employed. Although those methods have been employed in other fields, this is one of the earliest studies that employed those techniques in the context of traffic safety. Results: The results highlighted that the nonparametric kernel-based method outperforms the semi-parametric (single-index model) and the standard logit model based on the confusion matrices. To have a vision about the bandwidth selection method for removal of the irrelevant attributes in nonparametric approach, we added some noisy predictors to the models and a comparison was made. Extensive discussion has been made in the content of this study regarding the methodological approach of the models. Conclusion: To summarize, alcohol and drug involvement, driving on non-level grade, and bad lighting conditions are some of the factors that increase the likelihood of pedestrian crash severity. This is one of the earliest studies that implemented the methods in the context of transportation problems. The nonparametric method is especially recommended to be used in the field of traffic safety when there are uncertainties regarding the importance of predictors as the technique would automatically drop unimportant predictors.

The Generalised Plug-in Algorithm for the Diffeomorphism Kernel Estimate

The optimal value of the smoothing parameter of the Kernel estimator can be obtained by the well known Plug-in algorithm. The optimality is realised in the sense of Mean Integrated Square Error (MISE). In this paper, we propose to generalise this algorithm to the case of the difficult problem of the estimation of a distribution which has a bounded support. The proposed algorithm consists in searching the optimal smoothing parameter by iterations from the expression of MISE of the kernel-diffeomorphism estimator. By some simulations applied to some distribution having a support bounded and semi bounded, we show that the support of the pdf estimator respects the one of the theoretical distribution. We also prove that the proposed method minimizes the Gibbs phenomenon.

Selection of Optimal Smoothing Parameters in Mixed Estimator of Kernel and Fourier Series in Semiparametric Regression

In this article, we propose a new method of selecting smoothing parameters in semiparametric regression. This method is used in semiparametric regression estimation where the nonparametric component is partially approximated by multivariable Fourier Series and partly approached by multivariable Kernel. Selection of smoothing parameters using the method with Generalized Cross-Validation (GCV). To see the performance of this method, it is then applied to the data drinking water quality sourced from Regional Drinking Water Company (PDAM) Surabaya by using Fourier Series with trend and Gaussian Kernel. The results showed that this method contributed a good performance in selecting the optimal smoothing parameters.