Simulation evaluation of small samples based on grey estimation and improved bootstrap

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Wenguang Yang ◽  
Lianhai Lin ◽  
Hongkui Gao
Keyword(s):  
Similarity Measure ◽  
Bootstrap Method ◽  
Grey System Theory ◽  
Small Sample ◽  
Point Estimation ◽  
Small Samples ◽  
Content Type ◽  
Relational Similarity ◽  
Simulation Evaluation ◽  
Grey Relational

PurposeTo solve the problem of simulation evaluation with small samples, a fresh approach of grey estimation is presented based on classical statistical theory and grey system theory. The purpose of this paper is to make full use of the difference of data distribution and avoid the marginal data being ignored.Design/methodology/approachBased upon the grey distribution characteristics of small sample data, the definition about a new concept of grey relational similarity measure comes into being. At the same time, the concept of sample weight is proposed according to the grey relational similarity measure. Based on the new definition of grey weight, the grey point estimation and grey confidence interval are studied. Then the improved Bootstrap resampling is designed by uniform distribution and randomness as an important supplement of the grey estimation. In addition, the accuracy of grey bilateral and unilateral confidence intervals is introduced by using the new grey relational similarity measure approach.FindingsThe new small sample evaluation method can realize the effective expansion and enrichment of data and avoid the excessive concentration of data. This method is an organic fusion of grey estimation and improved Bootstrap method. Several examples are used to demonstrate the feasibility and validity of the proposed methods to illustrate the credibility of some simulation data, which has no need to know the probability distribution of small samples.Originality/valueThis research has completed the combination of grey estimation and improved Bootstrap, which makes more reasonable use of the value of different data than the unimproved method.

scholarly journals Dynamic Assessment of Vibration of Tooth Modification Gearbox Using Grey Bootstrap Method

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Hui-liang Wang ◽  
Xiao-zhong Deng ◽  
Ju-bo Li ◽  
Jian-jun Yang
Keyword(s):  
Systematic Error ◽  
Performance Optimization ◽  
Bootstrap Method ◽  
Dynamic Assessment ◽  
Grey System Theory ◽  
Small Sample ◽  
Error Measure ◽  
True Value ◽  
Dynamic Uncertainty ◽  
Tooth Modification

The correlation analysis between gear modification and vibration characteristics of transmission system was difficult to quantify; a novel small sample vibration of gearbox prediction method based on grey system theory and bootstrap theory was presented. The method characterized vibration base feature of tooth modification gearbox by developing dynamic uncertainty, estimated true value, and systematic error measure, and these parameters could indirectly dynamically evaluate the effect of tooth modification. The method can evaluate the vibration signal of gearbox with installation of no tooth modification gear and topological modification gear, respectively, considering that 100% reliability is the constraints condition and minimum average uncertainty is the target value. Computer simulation and experiment results showed that vibration amplitude of gearbox was decreased partly due to topological tooth modification, and each value of average dynamic uncertainty, mean true value, and systematic error measure was smaller than the no tooth modification value. The study provided an important guide for tooth modification, dynamic performance optimization.

Study on the second grey relational grade and its properties

Kybernetes ◽  
2010 ◽  
Vol 39 (8) ◽  
pp. 1330-1335 ◽  
Author(s):  
Yan Ma
Keyword(s):  
System Theory ◽  
Design Methodology ◽  
Grey System Theory ◽  
Forecasting Model ◽  
Grey System ◽  
Content Type ◽  
Grey Forecasting ◽  
Grey Relational Grade ◽  
Grey Relational ◽  
Practical Implications

PurposeThe purpose of this paper is to propose a second relational grade based on the general grey relational grade and analyze several of its properties.Design/methodology/approachGrey system theory. The paper proposes and studies second grey relational grade, establishes second grey relational formula, and studies several characteristics of second grey relational formula.FindingsProposing a second relational grade proved it could solve the problem of the parallelism partly and weaken relativity of space position.Research limitations/implicationsUntil now, the problem of the consistency could not be solved, nor could the problem of the effect which keeps the sequence the same.Practical implicationsThe precision of the grey forecasting model could be strengthened if used in the forecasting model.Originality/valueThe general relational grade only thinks over the relation between two sequences but does not involve the relation in one sequence. The second relational grade considers these two, so if the forecasting model is established with it, the model should be more exact.

scholarly journals Linear Regression Estimation Methods for Inferring Standard Values of Snow Load in Small Sample Situations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xudong Wang ◽  
Jitao Yao
Keyword(s):  
Linear Regression ◽  
Coefficient Of Variation ◽  
Small Sample ◽  
Point Estimation ◽  
Estimation Methods ◽  
Small Samples ◽  
Unbiased Estimation ◽  
Regression Estimation ◽  
Snow Load ◽  
Standard Values

The aim of this paper is to establish a new method for inferring standard values of snow load in small sample situations. Due to the incomplete meteorological data in some areas, it is often necessary to infer the standard values of snow load in the conditions of small samples in engineering, but the point estimation methods of classical statistics adopted till now do not take into account the influences of statistical uncertainty, and the inference results are always aggressive. In order to overcome the above shortcomings, according to the basic principle of optimal linear unbiased estimation and invariant estimation of the minimum type I distribution parameters and the tantile, using the least square method, the linear regression estimation methods for inferring standard values of snow load in small sample situations are proposed, which can take into account two cases such as parameter-free and known coefficient of variation, and the predicted formulas of snow load standard values are given, respectively. Through numerical integration and Monte Carlo numerical simulation, the numerical table of correlation coefficients is established, which is more convenient for the direct application of inferential formulas. According to the results of theoretical analysis and examples, when using the indirect point estimation methods to infer the standard values of snow load in the conditions of small samples, the inference results are always small. The linear regression estimation method is suitable for inferring standard values of snow load in the conditions of small samples, which can give more reasonable results. When using the linear regression estimation to infer standard values of snow load in practical application, even if the coefficient of variation is unknown, it can set the upper limit value of the coefficient of variation according to the experience; meanwhile, according to the parameter-free and known coefficient of variation, the estimation is carried out, respectively, and the smaller value of the two is taken as the final estimate. The method can be extended to the statistical inference of variable load standard values such as wind load and floor load.

Hospital readmission prediction based on improved feature selection using grey relational analysis and LASSO

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nor Hamizah Miswan ◽  
Chee Seng Chan ◽  
Chong Guan Ng
Keyword(s):  
Feature Selection ◽  
Grey Relational Analysis ◽  
Hospital Readmission ◽  
Grey System Theory ◽  
Feature Subset ◽  
Selection Algorithm ◽  
Feature Selection Algorithm ◽  
Content Type ◽  
Relational Analysis ◽  
Grey Relational

PurposeThis paper develops a robust hospital readmission prediction framework by combining the feature selection algorithm and machine learning (ML) classifiers. The improved feature selection is proposed by considering the uncertainty in patient's attributes that leads to the output variable.Design/methodology/approachFirst, data preprocessing is conducted which includes how raw data is managed. Second, the impactful features are selected through feature selection process. It started with calculating the relational grade of each patient towards readmission using grey relational analysis (GRA) and the grade is used as the target values for feature selection. Then, the influenced features are selected using the Least Absolute Shrinkage and Selection Operator (LASSO) method. This proposed method is termed as Grey-LASSO feature selection. The final task is the readmission prediction using ML classifiers.FindingsThe proposed method offered good performances with a minimum feature subset up to 54–65% discarded features. Multi-Layer Perceptron with Grey-LASSO gave the best performance.Research limitations/implicationsThe performance of Grey-LASSO is justified in two readmission datasets. Further research is required to examine the generalisability to other datasets.Originality/valueIn designing the feature selection algorithm, the selection on influenced input variables was based on the integration of GRA and LASSO. Specifically, GRA is a part of the grey system theory, which was employed to analyse the relation between systems under uncertain conditions. The LASSO approach was adopted due to its ability for sparse data representation.

Applying grey system theory to evaluate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries

2016 ◽  
Vol 6 (2) ◽  
pp. 143-168 ◽  
Author(s):  
Wuwei Li
Keyword(s):  
System Theory ◽  
Grey System Theory ◽  
High Tech ◽  
Grey System ◽  
Content Type ◽  
Relational Analysis ◽  
Panel Data Regression ◽  
Data Regression ◽  
Grey Relational ◽  
The Relationship

Purpose – For the studies whose purposes are to evaluate the relationship between industrial characteristics and innovation activities of the enterprises, there are some limitations in the measures of industrial characteristics and using traditional statistical techniques. The purpose of this paper is to investigate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries using grey system theory. The research results show that grey system theory is suitable to investigate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries. Design/methodology/approach – This paper proposes the measures of industrial characteristics and innovation capabilities of high-tech enterprises. First, based on the data on Chinese large and medium-sized high-tech enterprises for the period of 2011-2013, this paper applies grey relational analysis to identify the relatively most important indexes on affecting innovation capabilities of Chinese high-tech enterprises. Second, based on the results from grey relational analysis, this study draws a ranking of the five Chinese high-tech industries in terms of innovation capabilities by grey decision making. Finally, based on the results from grey decision making, this study applies GM (0, N) model to investigate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries. Findings – The results of this study show that in the evaluation indexes system of innovation capabilities of high-tech enterprises, personnel in R & D institutions, R & D personnel, internal expenditure on R & D, expenditure on new product development, expenditure on technology imports, expenditure on technology renovation, and expenditure on technology assimilation and absorption are relatively most important elements affecting innovation capabilities of Chinese high-tech enterprises. In addition, the two top ranking on innovation capabilities are manufacture of electronic equipment and communication equipment, and manufacture of medicines. At last, the findings indicate that in the measures of industrial characteristics, the three top ranking on affecting innovation capabilities of Chinese high-tech enterprises are R & D intensity, technology absorption intensity of indigenous high-tech enterprises and foreign-invested enterprises size. The opening level is in the middle position. Technology intensity, market concentration, and state-owned enterprises size are the three bottom ranking on affecting innovation capabilities of Chinese high-tech enterprises. Research limitations/implications – This study has some limitations. First, this study is limited to Chinese high-tech industries. The findings may not be applicable to other countries’ high-tech industries. Further studies with other countries’ high-tech industries could be extended and examined how industrial characteristics affect innovation capabilities of the firms in these industries. Second, the measures of industrial characteristics proposed in this study are somewhat theoretically weak. In the future, the authors will further improve the current analysis, and develop the measures of industrial characteristics. Finally, with the advent of the more data with the consistent statistical coverage released by China’s National Bureau of Statistics during the more continuous years, other methods, such as panel data regression model in econometrics could be used to evaluate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries. By then, the scholars can compare the results from grey system theory and those from panel data regression model in econometrics. Practical implications – Appropriate industrial environment is favorable for Chinese high-tech enterprises to feed their innovation capabilities. Scientific evaluation on the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries is of great significance for Chinese high-tech enterprises in exerting technological catch-up and promoting their competitive advantage. The purposed measures of industrial characteristics and innovation capabilities of high-tech enterprises in this paper, and combined methodology based on grey system theory could be applied to evaluate the relationship between industrial characteristics and innovation capabilities of Chinese high-tech enterprises. Originality/value – This paper proposes the measures of industrial characteristics and innovation capabilities of high-tech enterprises, and uses grey system theory to evaluate the relationship between industrial characteristics and innovation capabilities within Chinese high-tech industries.

Using performance templates for manager and employee learning – in-action

2014 ◽  
Vol 46 (2) ◽  
pp. 100-107
Author(s):  
Paul Lyons ◽  
Randall P. Bandura
Keyword(s):  
Performance Improvement ◽  
Empirical Support ◽  
Small Sample ◽  
Small Samples ◽  
Content Type ◽  
Sequence Of Events ◽  
Consistent Performance ◽  
And Performance ◽  
Employee Groups ◽  
Employee Learning

Purpose – This article demonstrates how the performance improvement process, performance templates, may be used for both manager and employee learning. The paper explains the concept, offers theoretical support for it, gives evidence of the efficacy of the process, and explains, in detail, how the process may be applied. Design/methodology/approach – The approach is to present or demonstrate what performance templates are and how a manager and a group of employees work together to create them and use them in the field. The paper presents the approach, explains how it connects with theory, offers empirical support for performance templates, and gives a sequence of events as to their creation and use. Findings – The findings indicate that, in general, the learning and performance approach, performance templates offer an influential and practical tool for both manager and employee learning, and consistent performance improvement. The approach has many applications, although recent research relies mostly on its use in sales organizations. Research limitations/implications – Primarily, the performance template approach has been used with small samples of learners. In the extant studies of the approach, small sample sizes limit the value of statistical analysis. Practical implications – The approach has not been tested with large employee groups (more than 25). The method is labor-intensive and time consuming. Large groups of participants would compromise the use of the approach as individual employee participation could be limited. Originality/value – Performance templates add to the arsenal of tools and methods available to trainers and managers. There is some empirical support for the approach. Performance templates represent both a learning approach and a performance improvement approach as managers and their employees work jointly to create learning and change.

The proof of a new modified grey relational grade

2016 ◽  
Vol 6 (2) ◽  
pp. 180-186 ◽  
Author(s):  
Kunli Wen
Keyword(s):  
System Theory ◽  
Grey Relational Analysis ◽  
Design Methodology ◽  
Grey System Theory ◽  
Grey System ◽  
Content Type ◽  
The Past ◽  
Relational Analysis ◽  
Grey Relational Grade ◽  
Grey Relational

Purpose – Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications. However, in one article published in 2007, which applied the previous grey relational grade to environmental protection fields and some results had been found. After studied it carefully, the author found that the grey relational grade in the paper was not the previous grey relational grade. According to the mathematics logic, it must first prove the proposed grey relational grade satisfies the four axioms in grey relational analysis, and then the author can say that the achieved results are reasonable and correct. The paper aims to discuss these issues. Design/methodology/approach – The paper lists the rational and regular grey relational grade that had been published in the past, and used the four axioms in grey system theory to prove the Pai’s grey relational grade that satisfy the four axioms steps by steps. Findings – Through the detail proof of the proposed grey relational grade in Pai’s paper, it indeed satisfies the four axioms in grey relational grade. Research limitations/implications – The paper had enhanced the correctness and reasonableness of that paper, and let the grey relational grade, which appear in Pai’s paper is legitimate and correct grey relational grade in grey system theory. Originality/value – The paper had identified that Pai’s grey relational grade is a rational and regular grey relational grade in grey system theory, and it proves that the results in Pai’s paper are correct and reasonable.

The status of traditional medicine and national medicine in different areas of the China in 2011 with grey clustering analysis

2014 ◽  
Vol 4 (2) ◽  
pp. 273-286 ◽  
Author(s):  
Lizhong Duan ◽  
Gu-man Duan ◽  
Qi Lu ◽  
Jun Duan ◽  
Li-yun XIE ◽  
...  
Keyword(s):  
Chinese Medicine ◽  
Traditional Medicine ◽  
Grey Relational Analysis ◽  
Clustering Analysis ◽  
Grey System Theory ◽  
Chinese Traditional Medicine ◽  
Content Type ◽  
Relational Analysis ◽  
Grey Clustering ◽  
Grey Relational

Purpose – The purpose of this paper is to improve the development of the Chinese traditional medicine (included the ethnic minority's medicine in China), it can raise the level of health for people, carry forward the culture of our nation, accelerate the economic development, promote social harmony and is very significant. Design/methodology/approach – In this paper, the factor which influences the development of the Chinese traditional medicine in these areas of China is analysed by the method called the grey relational analysis and grey clustering analysis. Findings – It is known that the comparative situation of each otherof the development of the Chinese traditional medicine in these areas. The causation is analysed. Practical implications – The behavioural mechanisms information which is effected by the traditional Chinese medicine (included ethnic minority medicine) is incomplete. Its inherent meaning is not clear. So it is reasonable to use the method called the grey relational analysis grey clustering analysis to study. Analysing the causes and giving countermeasures according to the results could propose some suggestions for the further development of Chinese medicine (including the national medicine) industry. Originality/value – The grey system theory was applied in medical management. The application of study results, the development of the Chinese traditional medicine (included the ethnic minority's medicine in China) is improved.

The most livable city selection in Turkey with the grey relational analysis

2020 ◽  
Vol 10 (4) ◽  
pp. 529-544 ◽  
Author(s):  
Erkan Kose ◽  
Danışment Vural ◽  
Gulcin Canbulut
Keyword(s):  
System Theory ◽  
Grey Relational Analysis ◽  
Complex Problem ◽  
Grey System Theory ◽  
Grey System ◽  
Content Type ◽  
Relational Analysis ◽  
Decision Points ◽  
Criteria Weights ◽  
Grey Relational

PurposeThis study has two main objectives: (1) to expand the application areas of grey system theory and (2) to select the most livable city in Turkey.Design/methodology/approachChoosing the most livable city is a complex problem that requires many criteria to be considered. It is important to select decision points according to which the criteria selection will be made and to what extent the criteria will affect the evaluation. For this purpose, a questionnaire was prepared to determine the criteria to be used in the assessment. The survey results were evaluated by the factor analysis (FA) and it was found that the criteria included in the survey were grouped under seven factors. Then, criteria weights were assigned to the determined criteria using the analytic hierarchy process (AHP). At the last stage, Turkey's six most popular cities are graded using the grey relational analysis (GRA) to reduce the uncertainty existing in the process of evaluation.FindingsThe obtained results indicated that the most livable city in Turkey is Istanbul. Istanbul is followed by Izmir, Antalya, Eskisehir, Bursa and Ankara, respectively. Considering that Istanbul is a center of attraction in many respects, this result is not a surprise for many people. It is also observed that the results obtained overlap with similar studies in the literature.Originality/valueGrey system theory and grey numbers have not been previously used to select the most livable city. With this aspect, this study has expanded the application of grey system theory and made an important contribution to the literature.

An improved bootstrap method introducing error ellipse for numerical analysis of fatigue life parameters

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Haiyan Ge ◽  
Xintian Liu ◽  
Yu Fang ◽  
Haijie Wang ◽  
Xu Wang ◽  
...  
Keyword(s):  
Normal Distribution ◽  
Bootstrap Method ◽  
Small Samples ◽  
Estimation Of Parameters ◽  
Error Ellipse ◽  
Content Type ◽  
Ellipse Model ◽  
Ellipse Method ◽  
Virtual Samples ◽  
The Bootstrap Method

Purpose The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve. Design/methodology/approach Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution. Findings By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method. Originality/value The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products.

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