We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be c...We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.展开更多
This paper focuses on a very important point which consists in evaluating experimental data prior to their use for chemical process designs. Hexafluoropropylene P, ρ, T data measured at 11 temperatures from 263 to 36...This paper focuses on a very important point which consists in evaluating experimental data prior to their use for chemical process designs. Hexafluoropropylene P, ρ, T data measured at 11 temperatures from 263 to 362 K and at pressures up to 10 MPa have been examined through a consistency test presented herein and based on the use of a methodology implying both neural networks and Virial equation. Such a methodology appears as very powerful to identify erroneous data and could be conveniently handled for quick checks of databases previously to modeling through classical thermodynamic models and equations of state. As an application to liquid and vapor phase densities of hexafluoropropylene, a more reliable database is provided after removing out layer data.展开更多
In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For exampl...In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.展开更多
Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-v...Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.展开更多
Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degrad...Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degradation mechanism of the RET is the same as the one of the normal stress condition. In order to check the consistency of two mechanisms, we conduct two enhancement tests with a missile servo system as an object of the study, and preprocess two sets of test data to establish the accelerated degradation models regarding the temperature change rate that is assumed to be the main applied stress of the servo system during the natural storage. Based on the accelerated degradation models and natural storage profile of the servo system, we provide and demonstrate a procedure to check the consistency of two mechanisms by checking the correlation and difference of two sets of degradation data. The results indicate that the two degradation mechanisms are significantly consistent with each other.展开更多
Phase equilibrium in binary gas + water mixtures over wide ranges of temperatures and pressures are modeled and tested for thermodynamic consistency. For modeling, the Peng-Robinson equation of state was used and the ...Phase equilibrium in binary gas + water mixtures over wide ranges of temperatures and pressures are modeled and tested for thermodynamic consistency. For modeling, the Peng-Robinson equation of state was used and the Wong-Sandler mixing rules were incorporated into the equation of state parameters. In the Wong-Sandler mixing rules the van Laar model for the excess Gibbs energy was applied. In addition, a reasonable and flexible method is applied to test the thermodynamic consistency of pressure-temperature-concentration(P-T-x) data of these binary mixtures.Modeling is found acceptable in all cases, meaning that deviations in correlating the pressure and the gas phase concentration are low. For all cases the thermodynamic consistency method gives a clear conclusion about consistency or inconsistency of a set of experimental P-T-x data.展开更多
We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and ...We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.展开更多
Genetic association studies usually apply the simple chi-square (χ<sup>2</sup>)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotyp...Genetic association studies usually apply the simple chi-square (χ<sup>2</sup>)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotypes and phenotypes are independent. So, the conventional χ<sup>2</sup>-test does not consider the increased risk of an individual carrying the increasing number of disease responsible allele (a particular genotype). But, the association tests should be performed with the consideration of this disease risk according to the mode of inheritance (additive, dominant, recessive). Practical demonstration of the two possible methods for considering such order or trends in contingency tables of genetic association studies using SNP genotype data is the purpose of this paper. One method is by pooling the genotypes, and the other is scoring the individual genotypes, based on the disease risk according to the inheritance pattern. The results show that the p-values obtained from both the methods are similar for the dominant and recessive models. The other important features of the methods were also extracted using the SNP genotype data for different inheritance patterns.展开更多
Regression estimates are biased when potential confounders are omitted or when there are other similar risks to validity.The instrumental variable(IV)method can be used instead to obtain less biased estimates or to st...Regression estimates are biased when potential confounders are omitted or when there are other similar risks to validity.The instrumental variable(IV)method can be used instead to obtain less biased estimates or to strengthen causal inferences.One key assumption critical to the validity of the IV method is the exclusion assumption,which requires instruments to be correlated with the outcome variable only through endogenous predictors.The chi-square test of model fit is widely used as a diagnostic test for this assumption.Previous simulation studies assessed the power of this diagnostic test only in situations with strong violations of the exclusion assumption.However,low to moderate levels of assumption violation are not uncommon in reality,especially when the exclusion assumption is violated indirectly.In this study,we showed through Monte Carlo simulations that the chi-square model fit test suffered from a severe lack of power(<30%)to detect violations of the exclusion assumption when the level of violation was of typical size,and the IV causal inferences were severely inaccurate and misleading in this case.We thus advise using the IV method with caution unless there is a chance for thorough assumption diagnostics,like in meta-analyses or experiments.展开更多
In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete informat...In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.展开更多
Image segmentation is a key and fundamental problem in image processing,computer graphics,and computer vision.Level set based method for image segmentation is used widely for its topology flexibility and proper mathem...Image segmentation is a key and fundamental problem in image processing,computer graphics,and computer vision.Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation.However,poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation.In this paper,we present a region consistency constraint term to measure the regional consistency on both sides of the boundary,this term defines the boundary of the image within a range,and hence increases the stability of the level set model.The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary.Furthermore,this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour.The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.展开更多
In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential...In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential residual Chi-square test and applies to fault detection of an integrated navigation system.The simulation result shows that the algorithm can accurately detect the fault information of global positioning system(GPS),eliminate the influence of false alarm and missed detection on filter,and enhance fault tolerance of integrated navigation systems.展开更多
A formal model representing the navigation behavior of a Web application as the Kripke structure is proposed and an approach that applies model checking to test case generation is presented. The Object Relation Diagra...A formal model representing the navigation behavior of a Web application as the Kripke structure is proposed and an approach that applies model checking to test case generation is presented. The Object Relation Diagram as the object model is employed to describe the object structure of a Web application design and can be translated into the behavior model. A key problem of model checking-based test generation for a Web application is how to construct a set of trap properties that intend to cause the violations of model checking against the behavior model and output of counterexamples used to construct the test sequences. We give an algorithm that derives trap properties from the object model with respect to node and edge coverage criteria.展开更多
This paper introduces uncertainty theory to deal with non-deterministic factors in ranking alternatives. The uncertain variable method (UVM) and the definition of consistency for uncertainty comparison matrices are pr...This paper introduces uncertainty theory to deal with non-deterministic factors in ranking alternatives. The uncertain variable method (UVM) and the definition of consistency for uncertainty comparison matrices are proposed. A simple yet pragmatic approach for testing whether or not an uncertainty comparison matrix is consistent is put forward. In cases where an uncertainty comparison matrix is inconsistent, an algorithm is used to generate consistent matrix. And then the consistent uncertainty comparison matrix can derive the uncertainty weights. The final ranking is given by uncertainty weighs if they are acceptable;otherwise we rely on the ranks of expected values of uncertainty weights instead. Three numerical examples including a hierarchical (AHP) decision problem are examined to illustrate the validity and practicality of the proposed methods.展开更多
The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of c...The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.展开更多
基金the National Natural Science Foundation of China (10571139)
文摘We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.
文摘This paper focuses on a very important point which consists in evaluating experimental data prior to their use for chemical process designs. Hexafluoropropylene P, ρ, T data measured at 11 temperatures from 263 to 362 K and at pressures up to 10 MPa have been examined through a consistency test presented herein and based on the use of a methodology implying both neural networks and Virial equation. Such a methodology appears as very powerful to identify erroneous data and could be conveniently handled for quick checks of databases previously to modeling through classical thermodynamic models and equations of state. As an application to liquid and vapor phase densities of hexafluoropropylene, a more reliable database is provided after removing out layer data.
文摘In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.
文摘Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.
基金supported by the Natural Science Foundation of Hunan Province(2018JJ2282)
文摘Reliability enhancement testing(RET) is an accelerated testing which hastens the performance degradation process to surface its inherent defects of design and manufacture. It is an important hypothesis that the degradation mechanism of the RET is the same as the one of the normal stress condition. In order to check the consistency of two mechanisms, we conduct two enhancement tests with a missile servo system as an object of the study, and preprocess two sets of test data to establish the accelerated degradation models regarding the temperature change rate that is assumed to be the main applied stress of the servo system during the natural storage. Based on the accelerated degradation models and natural storage profile of the servo system, we provide and demonstrate a procedure to check the consistency of two mechanisms by checking the correlation and difference of two sets of degradation data. The results indicate that the two degradation mechanisms are significantly consistent with each other.
基金the National Council for Scientific and Technological Research,CONICYT,for its grant FONDECYT 3020020the Center for Technological Information (La Serena-Chile) for computer and library support+1 种基金CAF thanks the Direction of Research of the University of Concepción for the support through the research grant DIUC 211.011.054-1.0JOV thanks the University of La Serena for especialsupport
文摘Phase equilibrium in binary gas + water mixtures over wide ranges of temperatures and pressures are modeled and tested for thermodynamic consistency. For modeling, the Peng-Robinson equation of state was used and the Wong-Sandler mixing rules were incorporated into the equation of state parameters. In the Wong-Sandler mixing rules the van Laar model for the excess Gibbs energy was applied. In addition, a reasonable and flexible method is applied to test the thermodynamic consistency of pressure-temperature-concentration(P-T-x) data of these binary mixtures.Modeling is found acceptable in all cases, meaning that deviations in correlating the pressure and the gas phase concentration are low. For all cases the thermodynamic consistency method gives a clear conclusion about consistency or inconsistency of a set of experimental P-T-x data.
文摘We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.
文摘Genetic association studies usually apply the simple chi-square (χ<sup>2</sup>)-test for testing association between a single-nucleotide polymorphism (SNP) and a particular phenotype, assuming the genotypes and phenotypes are independent. So, the conventional χ<sup>2</sup>-test does not consider the increased risk of an individual carrying the increasing number of disease responsible allele (a particular genotype). But, the association tests should be performed with the consideration of this disease risk according to the mode of inheritance (additive, dominant, recessive). Practical demonstration of the two possible methods for considering such order or trends in contingency tables of genetic association studies using SNP genotype data is the purpose of this paper. One method is by pooling the genotypes, and the other is scoring the individual genotypes, based on the disease risk according to the inheritance pattern. The results show that the p-values obtained from both the methods are similar for the dominant and recessive models. The other important features of the methods were also extracted using the SNP genotype data for different inheritance patterns.
基金supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515011986)National Natural Science Foundation of China(Grant No.31700986).
文摘Regression estimates are biased when potential confounders are omitted or when there are other similar risks to validity.The instrumental variable(IV)method can be used instead to obtain less biased estimates or to strengthen causal inferences.One key assumption critical to the validity of the IV method is the exclusion assumption,which requires instruments to be correlated with the outcome variable only through endogenous predictors.The chi-square test of model fit is widely used as a diagnostic test for this assumption.Previous simulation studies assessed the power of this diagnostic test only in situations with strong violations of the exclusion assumption.However,low to moderate levels of assumption violation are not uncommon in reality,especially when the exclusion assumption is violated indirectly.In this study,we showed through Monte Carlo simulations that the chi-square model fit test suffered from a severe lack of power(<30%)to detect violations of the exclusion assumption when the level of violation was of typical size,and the IV causal inferences were severely inaccurate and misleading in this case.We thus advise using the IV method with caution unless there is a chance for thorough assumption diagnostics,like in meta-analyses or experiments.
文摘In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator(MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.
基金supported in part by the NSFC-Zhejiang Joint Fund of the Integration of Informatization and Industrialization(U1609218)NSFC(61772312,61373078,61772253)+1 种基金the Key Research and Development Project of Shandong Province(2017GGX10110)NSF of Shandong Province(ZR2016FM21,ZR2016FM13)
文摘Image segmentation is a key and fundamental problem in image processing,computer graphics,and computer vision.Level set based method for image segmentation is used widely for its topology flexibility and proper mathematical formulation.However,poor performance of existing level set models on noisy images and weak boundary limit its application in image segmentation.In this paper,we present a region consistency constraint term to measure the regional consistency on both sides of the boundary,this term defines the boundary of the image within a range,and hence increases the stability of the level set model.The term can make existing level set models significantly improve the efficiency of the algorithms on segmenting images with noise and weak boundary.Furthermore,this constraint term can make edge-based level set model overcome the defect of sensitivity to the initial contour.The experimental results show that our algorithm is efficient for image segmentation and outperform the existing state-of-art methods regarding images with noise and weak boundary.
基金supported by the National Natural Science Foundation of China(6063403060702066)+1 种基金the Aerospace Science Foundation(20090853013)Fundmental Research Foundation of NWPU(JC201015),Soaring Star of NWPU
文摘In detecting system fault algorithms,the false alarm rate and undectect rate generated by residual Chi-square test can affect the stability of filters.The paper proposes a fault detection algorithm based on sequential residual Chi-square test and applies to fault detection of an integrated navigation system.The simulation result shows that the algorithm can accurately detect the fault information of global positioning system(GPS),eliminate the influence of false alarm and missed detection on filter,and enhance fault tolerance of integrated navigation systems.
基金Supported by the National Natural Science Foundation of China (60673115)the National Basic Research Program of China (973 Program) (2002CB312001)the Open Foundation of State Key Laboratory of Soft-ware Engineering (SKLSE05-13)
文摘A formal model representing the navigation behavior of a Web application as the Kripke structure is proposed and an approach that applies model checking to test case generation is presented. The Object Relation Diagram as the object model is employed to describe the object structure of a Web application design and can be translated into the behavior model. A key problem of model checking-based test generation for a Web application is how to construct a set of trap properties that intend to cause the violations of model checking against the behavior model and output of counterexamples used to construct the test sequences. We give an algorithm that derives trap properties from the object model with respect to node and edge coverage criteria.
文摘This paper introduces uncertainty theory to deal with non-deterministic factors in ranking alternatives. The uncertain variable method (UVM) and the definition of consistency for uncertainty comparison matrices are proposed. A simple yet pragmatic approach for testing whether or not an uncertainty comparison matrix is consistent is put forward. In cases where an uncertainty comparison matrix is inconsistent, an algorithm is used to generate consistent matrix. And then the consistent uncertainty comparison matrix can derive the uncertainty weights. The final ranking is given by uncertainty weighs if they are acceptable;otherwise we rely on the ranks of expected values of uncertainty weights instead. Three numerical examples including a hierarchical (AHP) decision problem are examined to illustrate the validity and practicality of the proposed methods.
基金supported by the Natural Science Foundation of China under Grant Nos.11071022,11028103,11231010,11471223,BCMIISthe Beijing Municipal Educational Commission Foundation under Grant Nos.KZ201410028030,KM201210028005Jishou University Subject in 2014(No:14JD035)
文摘The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.
