Fitting variogram models by weighted least squares

The method of weighted least squares is shown to be an appropriate way of fitting variogram models. The weighting scheme automatically gives most weight to early lags and down-weights those lags with a small number of pairs. Although weights are derived assuming the data are Gaussian (normal), they are shown to be still appropriate in the setting where data are a (smooth) transform of the Gaussian case. The method of (iterated) generalized least squares, which takes into account correlation between variogram estimators at different lags, offer more statistical efficiency at the price of more complexity. Weighted least squares for the robust estimator, based on square root differences, is less of a compromise.     

广义岭估计的直接解法

提出了广义岭估计的直接解法，该解法不需计算岭参数，可直接求得具有最小均方误差的解，并举例证实了该解法的优越性。     

地图数字化数据坐标变换的相关性分析

将用于求定地图数字化坐标转换参数的已知点的地面坐标和数字化坐标都当作观测值，用随有参数的条件平差求定转换参数，对采用4个已知点、9个已知点分别进行相似与仿射变换进行了分析，计算了格网点之间的相关系数，进一步分析了格网点间相关系数的分布规律，对转换后的坐标相关性进行了讨论。     

带缓和曲线的特大桥坐标计算及放样方法

介绍一种带缓和曲线的特大桥桥墩在测量坐标系下的坐标计算及桥墩放样方法 ,以及Leica全站仪在桥梁施工放样中的应用     

一个压力坐标下的海洋环流模式

A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-σ coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approxima tions. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations.     

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).     

Glacier development and topographic context

This paper analyses the topographic context of the remaining glaciated areas in the Maladeta Massif (Central Spanish Pyrenees). These ice‐covered surfaces have been incorporated into a geographic information system (GIS) in an attempt at correlating the presence of ice with a range of topographic variables obtained from a digital elevation model. The use of generalized additive models and binary regression tree models enabled us (i) to quantify the spatial variability in the distribution of glaciers attributable to characteristics of the local terrain, (ii) to investigate the interaction between the variables that account for the ice cover distribution and (iii) to map the probability of glacier development. Our results show that although the development of glaciers depends on regional climate conditions, the topographic context is of paramount importance in determining the location, extent, shape and recent evolution of each glacial body. Thus, the joint effect of altitude, exposure to incoming solar radiation, slope and mean curvature is able to explain more than 70 per cent of the observed variance. Copyright © 2006 John Wiley & Sons, Ltd.     

Modelling peak accelerations from earthquakes

This paper deals with the prediction of peak horizontal accelerations with emphasis on seismic risk and insurance concerns. Non‐linear mixed effects models are used to analyse well‐known earthquake data and the consequences of mis‐specifying assumptions on the error term are quantified. A robust fit of the usual model, using recently developed robust weighted maximum likelihood estimators, is presented. Outlying data are automatically identified and subsequently investigated. A more appropriate model accounting for the extreme value nature of the responses, is also developed and implemented. The implication on acceleration predictions is demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

一类双曲-抛物型方程的广义解

讨论了一类奇摄动双曲-抛物型方程广义初边值问题,在适当的条件下,用Galerkin方法研究了广义解的存在性、唯一性,同时得到了解的渐近估计式。