Generalized cross-validation for covariance model selection

A weighted cross-validation technique known in the spline literature as generalized cross-validation (GCV), is proposed for covariance model selection and parameter estimation. Weights for prediction errors are selected to give more importance to a cluster of points than isolated points. Clustered points are estimated better by their neighbors and are more sensitive to model parameters. This rational weighting scheme also provides a simplifying significantly the computation of the cross-validation mean square error of prediction. With small- to medium-size datasets, GCV is performed in a global neighborhood. Optimization of usual isotropic models requires only a small number of matrix inversions. A small dataset and a simulation are used to compare performances of GCV to ordinary cross-validation (OCV) and least-squares filling (LS).     

广义帕累托分布在广东重现期风速计算中的应用

利用广东省86个国家气象观测站建站以来近70a的逐月最大风速序列和近20a(1999—2018年)的逐月最大风速序列,基于POT抽样法,分别采用三参数广义帕累托分布函数对各站的重现期风速进行了概率计算,计算过程中三参数广义帕累托分布函数分别采用矩估计(MOM)、极大似然估计(MLE)、似然矩估计(LM)和概率权矩估计(PWM)等4种参数估计方法,结合表征参数估计优良性的指标:均方根误差RMSE、拟合相对偏差和显著性水平为0.05的科莫戈洛夫检验拟合适度指标K_f对拟合效果进行检验,结果表明:基于POT抽样的概率权矩估计(PWM)拟合效果最好。     

矩阵广义初等变换及其运用

提出了关于分块矩阵的广义初等变换这一概念,以此为工具简化了一些复杂矩阵问题的解决方法。     

复平面上广义插值多项式的平均逼近阶

研究了复平面上 ,广义 Hermite-Fejer插值多项式的收敛性。得到了其在空间 lp(| z| =1 ) (0 相似文献   

Generalized Laplace coefficients and Newcomb derivatives

It is shown how the generalized Laplace coefficients can be employed to deduce explicit formulas for ordinary and Newcomb derivatives of the Laplace coefficients.      

A GIHS-based spectral preservation fusion method for remote sensing images using edge restored spectral modulation

High spatial resolution and spectral fidelity are basic standards for evaluating an image fusion algorithm. Numerous fusion methods for remote sensing images have been developed. Some of these methods are based on the intensity–hue–saturation (IHS) transform and the generalized IHS (GIHS), which may cause serious spectral distortion. Spectral distortion in the GIHS is proven to result from changes in saturation during fusion. Therefore, reducing such changes can achieve high spectral fidelity. A GIHS-based spectral preservation fusion method that can theoretically reduce spectral distortion is proposed in this study. The proposed algorithm consists of two steps. The first step is spectral modulation (SM), which uses the Gaussian function to extract spatial details and conduct SM of multispectral (MS) images. This method yields a desirable visual effect without requiring histogram matching between the panchromatic image and the intensity of the MS image. The second step uses the Gaussian convolution function to restore lost edge details during SM. The proposed method is proven effective and shown to provide better results compared with other GIHS-based methods.     

BIBLIOGRAPHIE

Abstract

Time series modelling approaches are useful tools for simulating and forecasting hydrological variables and their change through time. Although linear time series models are common in hydrology, the nonlinear time series model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, has rarely been used in hydrology and water resources engineering. The GARCH model considers the conditional variance remaining in the residuals of the linear time series models, such as an ARMA or an ARIMA model. In the present study, the advantages of a GARCH model against a linear ARIMA model are investigated using three classes of the GARCH approach, namely Power GARCH, Threshold GARCH and Exponential GARCH models. A daily streamflow time series of the Matapedia River, Quebec, Canada, is selected for this study. It is shown that the ARIMA (13,1,4) model is adequate for modelling streamflow time series of Matapedia River, but the Engle test shows the existence of heteroscedasticity in the residuals of the ARIMA model. Therefore, an ARIMA (13,1,4)-GARCH (3,1) error model is fitted to the data. The residuals of this model are examined for the existence of heteroscedasticity. The Engle test indicates that the GARCH model has considerably reduced the heteroscedasticity of the residuals. However, the Exponential GARCH model seems to completely remove the heteroscedasticity from the residuals. The multi-criteria evaluation for model performance also proves that the Exponential GARCH model is the best model among ARIMA and GARCH models. Therefore, the application of a GARCH model is strongly suggested for hydrological time series modelling as the conditional variance of the residuals of the linear models can be removed and the efficiency of the model will be improved.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Modarres, R. and Ouarda, T.B.M.J., 2013. Modelling heteroscedasticty of streamflow times series. Hydrological Sciences Journal, 58 (1), 1–11.     

RESOLUTION OF MULTICOMPONENT FLUORESCENT MIXTURES BY ANALYSIS OF THE EXCITATION-EMISSION-FREQUENCY ARRAY

Fluorescence lifetime provides a third independent dimension of information for the resolution of totalluminescence spectra of multicomponent mixtures.The incorporation of this parameter into theexcitation-emission matrix(EEM)by the phase modulation technique results in a three-dimensionalexcitation-emission-frequency array (EEFA).Multicomponent analysis based on the three-dimensionalEEFA brings a qualitative change for the resolved spectra,i.e.individual spectra can be uniquely resolved,which is impossible with any two-dimensional analysis.In this paper we present a method for analyzingthe EEFA.We show mathematically that with the three-dimensional analysis of the EEFA individualspectra and lifetimes can be obtained.Our algorithm is developed in mathematical detail and isdemonstrated by its application to a two-component mixture.     

Nonlinear regional economic dynamics: continuous-time specification,estimation and stability analysis

This paper presents an innovative approach to the study of regional economic dynamics within a nonlinear continuous-time econometric framework—a generalized specification of the Lotka–Volterra system of equations. This specification, which accounts for interdependent behavior of three industrial sectors and spillover effects of activities in neighboring regions, is employed in an analysis of five Italian regions between 1980 and 2003. For these regions, we report estimation results, characterize the varying systems dynamics, analyze the models’ local and global stability properties, and determine via sensitivity analyses which structural features appear to exert the greatest influence on these properties.

Reaction-Diffusion Systems and Nonlinear Waves

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne et al. (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation. The importance of the derived results lies in the fact that numerous results on fractional reaction, fractional diffusion, anomalous diffusion problems, and fractional telegraph equations scattered in the literature can be derived, as special cases, of the results investigated in this article.