We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Be...We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Berry-Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment.Under the Cramér condition,we establish the Cramér-type moderate deviations of the MLE of the growth rate.We first derive a Berry-Esseen bound,a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean.Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry-Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.展开更多
In this study,the impact of the training sample selection method on the performance of fuzzy-based Possibilistic c-means(PCM)and Noise Clustering(NC)classifiers were examined and mapped the cumin and fennel rabi crop....In this study,the impact of the training sample selection method on the performance of fuzzy-based Possibilistic c-means(PCM)and Noise Clustering(NC)classifiers were examined and mapped the cumin and fennel rabi crop.Two training sample selection approaches that have been investigated in this study are“mean”and“individual sample as mean”.Both training sample techniques were applied to the PCM and NC classifiers to classify the two indices approach.Both approaches have been studied to decrease spectral information in temporal data processing.The Modified Soil Adjusted Vegetation Index 2(MSAVI-2)and Class-Based Sensor Independent Modified Soil Adjusted Vegetation Index-2(CBSI-MSAVI-2)have been considered to minimize soil background effects,enhancing vegetation detection accuracy,particularly in areas with sparse vegetation cover.The MMD(MeanMembership Difference)and RMSE(RootMean Square Error)approaches were used to measure the study’s accuracy.To illustrate that the classifier successfully describes classes,cluster validity(SSE)was also performed,and the variance parameter was computed to handle heterogeneity within cumin and fennel crop fields.For the calculation of RMSE,Sentinel-2 data was used as classified,whereas PlanetScope satellite data was utilized as the reference data set.The best result was obtained using the NC classifier with“individual sample as mean”using CBSI-MSAVI-2 temporal indices.For Fuzziness Factor(m)=1.1,the RMSE,MMD,Variance,and SSE values for the NC classifier using“individual sample as mean”on the CBSI-MSAVI-2 temporal indices for cumin were 0.00098,0.00162,0.02857,and 0.97143,respectively and for fennel were 0.00025,0.00248,0.10420,and 3.54286,respectively.展开更多
A degenerated U-statistic with rank 2 is known to converge in distribution to a weighted sum of independent chi-square random variables.However,a result for the asymptotic distribution of a degenerated Ustatistic with...A degenerated U-statistic with rank 2 is known to converge in distribution to a weighted sum of independent chi-square random variables.However,a result for the asymptotic distribution of a degenerated Ustatistic with rank higher than 2 is not available in the literature.We derive explicitly the asymptotic distribution of a degenerated U-statistic with any rank,which is useful for hypothesis testing when the test statistic is a degenerated U-statistic under null hypothesis.Interestingly,the limit for a degenerated U-statistic with rank higher than 2 is a weighted sum of independent polynomials of the standard normal random variables.展开更多
Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means...Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means of sample mean and sample variance,which vary with the reduced range of the epistemic parameter.The RCVSM and RCVSV can be computed by the same set of samples,thus no extra computational cost is introduced with respect to the computations of CVSM and CVSV.From the plots of RCVSM and RCVSV,accurate quantitative information on variance reductions of sample mean and sample variance can be read because of reduced upper bound of the range of the epistemic parameter.For general form of quadratic polynomial output,the analytical solutions of the original and the revised RIMs are given.Numerical example is employed and results demonstrate that the analytical results are consistent and accurate.An engineering example is applied to testify the validity and rationality of the revised RIMs,which can give instructions to the engineers about how to reduce variance of sample mean and sample variance by reducing the range of epistemic parameters.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11971361,12371275)。
文摘We study Berry-Esseen bounds and Cramér-type moderate deviations of a jump-type Cox-Ingersoll-Ross(CIR)process driven by a standard Wiener process and a subordinator.In the sub critical case,we obtain the best Berry-Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment.Under the Cramér condition,we establish the Cramér-type moderate deviations of the MLE of the growth rate.We first derive a Berry-Esseen bound,a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean.Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry-Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.
文摘In this study,the impact of the training sample selection method on the performance of fuzzy-based Possibilistic c-means(PCM)and Noise Clustering(NC)classifiers were examined and mapped the cumin and fennel rabi crop.Two training sample selection approaches that have been investigated in this study are“mean”and“individual sample as mean”.Both training sample techniques were applied to the PCM and NC classifiers to classify the two indices approach.Both approaches have been studied to decrease spectral information in temporal data processing.The Modified Soil Adjusted Vegetation Index 2(MSAVI-2)and Class-Based Sensor Independent Modified Soil Adjusted Vegetation Index-2(CBSI-MSAVI-2)have been considered to minimize soil background effects,enhancing vegetation detection accuracy,particularly in areas with sparse vegetation cover.The MMD(MeanMembership Difference)and RMSE(RootMean Square Error)approaches were used to measure the study’s accuracy.To illustrate that the classifier successfully describes classes,cluster validity(SSE)was also performed,and the variance parameter was computed to handle heterogeneity within cumin and fennel crop fields.For the calculation of RMSE,Sentinel-2 data was used as classified,whereas PlanetScope satellite data was utilized as the reference data set.The best result was obtained using the NC classifier with“individual sample as mean”using CBSI-MSAVI-2 temporal indices.For Fuzziness Factor(m)=1.1,the RMSE,MMD,Variance,and SSE values for the NC classifier using“individual sample as mean”on the CBSI-MSAVI-2 temporal indices for cumin were 0.00098,0.00162,0.02857,and 0.97143,respectively and for fennel were 0.00025,0.00248,0.10420,and 3.54286,respectively.
文摘A degenerated U-statistic with rank 2 is known to converge in distribution to a weighted sum of independent chi-square random variables.However,a result for the asymptotic distribution of a degenerated Ustatistic with rank higher than 2 is not available in the literature.We derive explicitly the asymptotic distribution of a degenerated U-statistic with any rank,which is useful for hypothesis testing when the test statistic is a degenerated U-statistic under null hypothesis.Interestingly,the limit for a degenerated U-statistic with rank higher than 2 is a weighted sum of independent polynomials of the standard normal random variables.
基金supported by the National Natural Science Foundation of China(Grant No.51175425)the Special Research Fund for the Doctoral Program of Higher Education of China(Grant No.20116102110003)
文摘Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means of sample mean and sample variance,which vary with the reduced range of the epistemic parameter.The RCVSM and RCVSV can be computed by the same set of samples,thus no extra computational cost is introduced with respect to the computations of CVSM and CVSV.From the plots of RCVSM and RCVSV,accurate quantitative information on variance reductions of sample mean and sample variance can be read because of reduced upper bound of the range of the epistemic parameter.For general form of quadratic polynomial output,the analytical solutions of the original and the revised RIMs are given.Numerical example is employed and results demonstrate that the analytical results are consistent and accurate.An engineering example is applied to testify the validity and rationality of the revised RIMs,which can give instructions to the engineers about how to reduce variance of sample mean and sample variance by reducing the range of epistemic parameters.
