On a stronger-than-best property for best prediction

The minimum mean squared error (MMSE) criterion is a popular criterion for devising best predictors. In case of linear predictors, it has the advantage that no further distributional assumptions need to be made, other then about the first- and second-order moments. In the spatial and Earth sciences, it is the best linear unbiased predictor (BLUP) that is used most often. Despite the fact that in this case only the first- and second-order moments need to be known, one often still makes statements about the complete distribution, in particular when statistical testing is involved. For such cases, one can do better than the BLUP, as shown in Teunissen (J Geod. doi: 10.1007/s00190-007-0140-6, 2006), and thus devise predictors that have a smaller MMSE than the BLUP. Hence, these predictors are to be preferred over the BLUP, if one really values the MMSE-criterion. In the present contribution, we will show, however, that the BLUP has another optimality property than the MMSE-property, provided that the distribution is Gaussian. It will be shown that in the Gaussian case, the prediction error of the BLUP has the highest possible probability of all linear unbiased predictors of being bounded in the weighted squared norm sense. This is a stronger property than the often advertised MMSE-property of the BLUP.     

A type of biased estimators for linear models with uniformly biased data

The objective of this paper is the comparison of various types of estimators that can be used in linear models with uniformly biased data. This particular case refers to adjustment problems where the available measurements are affected by a common, unknown and uniform offset. The classic least-squares (LS) unbiased estimators for this type of models are reviewed in detail, and some additional remarks on their properties and performance are given. Furthermore, a family of biased estimators for linear models with uniformly biased data is introduced, which has the potential to provide better performance (in terms of mean squared estimation error) than the ordinary LS unbiased solutions. A number of different regularization viewpoints that can be equivalently associated with these biased estimators are presented, along with a discussion on various selection strategies that can be employed for the choice of the regularization parameter that enters into the biased estimation algorithm.     

Least-squares collocation with covariance-matching constraints

Most geostatistical methods for spatial random field (SRF) prediction using discrete data, including least-squares collocation (LSC) and the various forms of kriging, rely on the use of prior models describing the spatial correlation of the unknown field at hand over its domain. Based upon an optimal criterion of maximum local accuracy, LSC provides an unbiased field estimate that has the smallest mean squared prediction error, at every computation point, among any other linear prediction method that uses the same data. However, LSC field estimates do not reproduce the spatial variability which is implied by the adopted covariance (CV) functions of the corresponding unknown signals. This smoothing effect can be considered as a critical drawback in the sense that the spatio-statistical structure of the unknown SRF (e.g., the disturbing potential in the case of gravity field modeling) is not preserved during its optimal estimation process. If the objective for estimating a SRF from its observed functionals requires spatial variability to be represented in a pragmatic way then the results obtained through LSC may pose limitations for further inference and modeling in Earth-related physical processes, despite their local optimality in terms of minimum mean squared prediction error. The aim of this paper is to present an approach that enhances LSC-based field estimates by eliminating their inherent smoothing effect, while preserving most of their local prediction accuracy. Our methodology consists of correcting a posteriori the optimal result obtained from LSC in such a way that the new field estimate matches the spatial correlation structure implied by the signal CV function. Furthermore, an optimal criterion is imposed on the CV-matching field estimator that minimizes the loss in local prediction accuracy (in the mean squared sense) which occurs when we transform the LSC solution to fit the spatial correlation of the underlying SRF.     

Least-squares prediction in linear models with integer unknowns

The prediction of spatially and/or temporal varying variates based on observations of these variates at some locations in space and/or instances in time, is an important topic in the various spatial and Earth sciences disciplines. This topic has been extensively studied, albeit under different names. The underlying model used is often of the trend-signal-noise type. This model is quite general and it encompasses many of the conceivable measurements. However, the methods of prediction based on these models have only been developed for the case the trend parameters are real-valued. In the present contribution we generalize the theory of least-squares prediction by permitting some or all of the trend parameters to be integer valued. We derive the solution for least-squares prediction in linear models with integer unknowns and show how it compares to the solution of ordinary least-squares prediction. We also study the probabilistic properties of the associated estimation and prediction errors. The probability density functions of these errors are derived and it is shown how they are driven by the probability mass functions of the integer estimators. Finally, we show how these multimodal distributions can be used for constructing confidence regions and for cross-validation purposes aimed at testing the validity of the underlying model. Dedicated to the memory of Dr. Tech.hc. Torben Krarup (1919–2005).     

最小二乘插值与拟合推估

简述了最小二乘插值法的原理及解算过程 ,逐步引入最小二乘纯推估的概念 ,讨论了滤波与推估的结合 ,进而导出了最小二乘拟合推估的一般模型 ,得出了“最小二乘插值是拟合推估的特殊情况”的结论 ,对最小二乘拟合推估的解析性进行了简要的讨论     

A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator

 A bound is established for the Euclidean norm of the difference between the best linear unbiased estimator and any linear unbiased estimator in the general linear model. The bound involves the spectral norm of the difference between the dispersion matrices of the two estimators, and the residual sum of squares, all evaluated at the assumed model, but is independent of the provenance of the observation vector at hand. The bound, a straightforward consequence of first principles in Gauss–Markov theory, generalizes previous results on the difference between the best linear unbiased estimator and the ordinary least-squares estimator. In a numerical example from repeated precise levelling, the bound is used to analyse the sensitivity of estimates of vertical motion to the choice of estimator. Received: 9 September 1999 / Accepted: 15 March 2002     

一个新的GNSS模糊度估计类

介绍了一类新的GNSS模糊度估计。因为该类遵循移去一恢复原理，称之为整数等变估计类。本文将说明整数等变估计类较整数估计类和线性无偏估计类的范围要大，同时给出一个相当有用的整数等变估计类的表达式。这个表达式揭示了整数等变估计类的结构，并显示该表达式如何在浮点解的基础上实现整数等变估计。最后还提出最优整数估计。     

基于误差补偿预测树的多光谱遥感图像无损压缩方法

预测树方法是一种有效的无损多光谱图像压缩技术,将自适应线性预测方法与传统预测树方法相结合,提出了一种多光谱遥感图像的误差补偿预测树压缩方法。该方法利用多光谱图像谱间的局部统计冗余和结构冗余建立自适应预测器,对传统预测树方法产生的误差进行补偿,从而进一步减少了多光谱图像的数据量;并且利用多光谱图像的局部平稳特性对算法进行了简化。实验结果表明,该方法得到的压缩比与原始预测树方法相比有明显提高,同时算法简化后可以使计算复杂度大幅度降低。     

Forecasting sea level anomalies from TOPEX/Poseidon and Jason-1 satellite altimetry

This paper aims at the prediction of both global mean sea level anomalies (SLAs) and gridded SLA data in the east equatorial Pacific obtained from TOPEX/Poseidon and Jason-1 altimetric measurements. The first prediction technique (denoted as LS) is based on the extrapolation of a polynomial-harmonic deterministic least-squares model describing a linear trend, annual and semi-annual oscillations. The second prediction method (denoted as LS + AR) is a combination of the extrapolation of a polynomial-harmonic model with the autoregressive forecast of LS residuals. In the case of forecasting global mean SLA data, both techniques allow one to compute the predictions of comparable accuracy (root mean square error for 1-month in the future is of 0.5 cm). In the case of predicting gridded SLA data, the LS + AR prediction method gains significantly better prediction accuracy than the accuracy obtained by the LS technique during El Niño 1997/1998, La Niña 1998/1999 and during normal conditions.     

模型误差平差补偿方法比较

在高精度数据处理中,模型误差是不可忽视的。针对模型误差,简单介绍了模型误差补偿的四种方法。通过某一实例四种方法的补偿比较发现在此例中最小二乘方法补偿效果最好,并分析解释了半参数法在此例中不适合的原因。     

基于Logistic模型的单点下沉预测应用研究

岩层与地表移动具有一定的规律,由于Knothe时间函数虽然可以预计地表下沉,但在预计中有描述地表下沉速度的不足,并且其函数复杂.研究矿区单点动态下沉过程对于地表建筑物的保护具有重要意义,本文采用Logistic模型拟合下沉曲线,得到了预计方程,结果表明预计精度较高.Logistic模型参数少,函数相对简单,计算结果表明...     

空间预测的地统计学框架(英文)

Geostatistics provides a coherent framework for spatial prediction and uncertainty assessment, whereby spatial dependence, as quantified by variograms, is utilized for best linear unbiased estimation of a regionalized variable at unsampied locations. Geostatistics for prediction of continuous regionalized variables is reviewed, with key methods underlying the derivation of major variants of uni-vafiate Kriging described in an easy-to-follow manner. This paper will contribute to demysti- fication and, hence, popularization of geostatistics in geoinformatics communities.     

Least squares adjustment and collocation

Summary For the estimation of parameters in linear models best linear unbiased estimates are derived in case the parameters are random variables. If their expected values are unknown, the well known formulas of least squares adjustment are obtained. If the expected values of the parameters are known, least squares collocation, prediction and filtering are derived. Hence in case of the determination of parameters, a least squares adjustment must precede a collocation because otherwise the collocation gives biased estimates. Since the collocation can be shown to be equivalent to a special case of the least squares adjustment, the variance of unit weight can be estimated for the collocation also. This estimate gives the scale factor for the covariance matrices being used in the collocation. In addition, the methods of testing hypotheses and establishing confidence intervals for the parameters of the least squares adjustment may be applied to the collocation.     

基于分类K—L变换的多波段遥感图像近无损压缩方法

去除空间和谱间相关性是多波段遥感图像压缩中的重要环节，为了得到更好的去相关效果，将矢量量化方法引入多波段遥感图像压缩中，以去除对应同一地物的波段矢量间的相关性，再通过分类K－L变换去除量化误差图像的变间相关性，对K－L变换后的特征图像采用预测树的方法进一步去除谱间结构相关性和空间相关性，实验结果表明，该方法可以取得很好的压缩效果。     

秩亏网伪逆平差值的修正估计

本文在[1]的基础上提出了秩亏的带权测量平差模型中禾知参数向量的一种线性有偏估计——秩亏网伪逆平差值的修正估计,并着重讨论了该估计在均方误差意义下改进最小二乘估计的优越性、可容许性及新产生的偏差。最后通过实例验证了所得结果。     

基于模糊隶属函数的参数稳健估计

参数估计过程经常遇到2个主要问题:一个是最小二乘与稳健估计不能兼顾最优无偏性和稳健性;另一个是非线性模型参数估计进行线性近似处理中带来的模型误差导致对粗差的错误鉴别和定位。针对以上2个问题,提出了基于模糊隶属函数的稳健估计方法。该方法通过隶属度加权来削弱个别粗差污染数据对参数估计结果的影响,从而达到提高参数估计稳健性的目的。分别用线性回归模型和非线性回归模型对该算法进行了验证,结果表明,该算法对粗差具有较好的抵抗能力,能够对参数进行稳健估计。     

径向基函数神经网络在GPS卫星钟差预报中的应用

GPS卫星钟在空中很容易受到诸多因素的影响,导致其钟差行为很难用线性模型,二次多项式模型,灰色模型等现有模型进行描述和实现可靠的高精度预报。本文利用径向基函数神经网络对几颗GPS卫星钟差连续进行了五分钟、一小时和一天的预报,分别取得了均方根误差优于0.4ns,0.5ns和1ns的预报精度,证明了文中径向基网络结构在钟差预报方面的可靠性。     

基于偏差矫正的有偏估计及其在GPS快速定位中的应用

基于偏差矫正的一般理论提出了不适定问题的新的有偏估计。在病态条件下,Gauss-Markov模型参数的最优线性无偏估计,即LS估计是不稳健的,所得估值方差较大,严重偏离真值。因此,文中放弃了对参数估计无偏性的限制,考虑有偏估计的偏差,结合偏差矫正的正则化解法的一般理论提出了一种新的基于偏差矫正的有偏估计;结合岭估计中参数的选择方法确定了替代矩阵。最后通过GPS动态定位算例,验证了新估计的稳定性和有效性。     

基于BP神经网络技术的区域短期地震预测模型研究

地震预测是一个世界性科学难题,特别是短期与临震预测的水平与社会需求相距甚远。论文在详细分析研究地震数据特征以及常规地震预测方法的基础上,提出了一种可以实现地震震级量化预测的新方法,此方法通过解算出地震参数和天文时变参数并建立地震预测模型,对未来预测周期内发生的最大地震震级进行量化预测。本文以实验区域为研究对象并选取6个月为预测周期,采用线性回归分析方法和常规BP神经网络方法进行研究。经回溯检验,其地震震级预测中误差分别为±0.78级和±0.61级,精度均有待提高。经过总结上述两种方法的优缺点,创新的提出了基于线性回归与神经网络技术的地震预测融合模型,回溯检验结果表明,融合模型的震级预测中误差为±0.41级,地震预测效果显著提高。     

污染误差模型下的测量数据处理理论

本文首先研究了污染误差模型的各种具体的误差表示形式,然后研究了误差服从污染误差模型时的平差准则。指出,当误差服从污染误差模型时选择均方差作为估计准则是合理的,并且符合传统的测量误差处理的观念。最后,推导了误差服从污染误差模型时,均方误差准则下的最佳估计,从而建立以均方误差准则为基础的污染误差模型下的测量数据处理理论。