非线性半参数模型最小二乘核估计的直接解法

基于非线性半参数模型最小二乘核估计,给出了其参数分量和非参数分量估计的构造式,导出了参数分量和非参数分量顾及二次项直接解法的计算公式。用实测数据进行计算,证明了对于非线性半参数模型最小二乘核估计,可采用顾及二次项的直接解法。     

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平衡损失下回归系数stein压缩估计的性质

在平衡损失风险函数准则下,研究线性模型中回归系数的stein估计优于最小二乘估计(LS)的充分必要条件,然后在pitman closeness(PC)准则下比较了stein估计相对于最小二乘估计的优良性。     

关于回归系数有偏估计的两个问题

本文讨论了回归系数有偏估计的两个问题。一是对文[2]提出的回归系数的一种新的有偏估计——根方估计作了一定改进,提出了广义根方估计,从理论上证明了广义根方估计能够比根方估计达到更低的均方误差,并且给出了求根方参数的一个公式。二是在一般协方差情形下,证明了回归系数广义岭估计的弱相合性、均方相合性与条件等价。     

Estimating Petroleum Resources Using Geo-Anchored Method--A Sensitivity Study

The Geo-anchored method, based on a moment-type estimator, has been developed for estimating parent population properties from a successive sample of discoveries. By substituting the expectation of the waiting time z _(n+1) of the (n + 1) ^th discovery to occurrence for an unknown parameter in the anchored method, the Geo-anchored method allows estimation of inclusion probabilities directly from observed data, thus eliminating the need for a priori selection of a value of N, R, or some other feature of the parent population. Because direct estimation of N and R requires an ordered sample, the Geo-anchored method is more sensitive to the data-generating process than the anchored method. This paper presents a sensitivity study on the Geo-anchored method. The test is based on simulated discovery sequences with different assumptions regarding discovery efficiency, exploration maturity, and the shape of the parent field size distribution. As a reference for comparison, estimates from the Horvitz–Thompson estimator also are presented.     

分层随机抽样下全球30 m火烧迹地产品验证

火烧迹地是全球及区域碳循环和气候变化等研究所需的重要参数之一,卫星遥感技术为快速获取大区域火烧迹地空间分布信息提供了有效手段。中国科学院基于Landsat系列卫星数据研发了首个30 m空间分辨率全球火烧迹地产品GABAM (Global Annual Burned Area Map)。遥感数据产品的精度验证对产品使用具有重要意义,迄今尚未有研究机构对GABAM产品精度进行独立评价和分析。为系统评价GABAM产品精度,利用2010年全球30 m空间分辨率火烧迹地产品(GABAM2010)开展精度验证研究工作,在全球和几个陆地生物群落中估算了产品精度,并探索了全球遥感专题产品精度验证的技术框架。基于分层随机抽样选择80个非重叠的泰森多边形区域TSA (Thiessen Scene Areas),采用误差矩阵和6个精度指标对GABAM2010产品做全面精度评价和分析,以满足火烧迹地产品用户的使用要求。结果表明:在全球范围内,GABAM2010产品的错分率和漏分率分别为24.32%和31.60%,总体精度为97.85%;由于数据质量(如条带、云)等的影响,火烧迹地的范围会被低估,对于较容易发生火灾的生物群落,如热带亚热带草原区域,GABAM2010产品精度较高;在生物群落内部,高密度火烧迹地区域的精度高于低密度火烧迹地区域。     

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Bayesian area-to-point kriging using expert knowledge as informative priors

Area-to-point (ATP) kriging is a common geostatistical framework to address the problem of spatial disaggregation or downscaling from block support observations (BSO) to point support (PoS) predictions for continuous variables. This approach requires that the PoS variogram is known. Without PoS observations, the parameters of the PoS variogram cannot be deterministically estimated from BSO, and as a result, the PoS variogram parameters are uncertain. In this research, we used Bayesian ATP conditional simulation to estimate the PoS variogram parameters from expert knowledge and BSO, and quantify uncertainty of the PoS variogram parameters and disaggregation outcomes. We first clarified that the nugget parameter of the PoS variogram cannot be estimated from only BSO. Next, we used statistical expert elicitation techniques to elicit the PoS variogram parameters from expert knowledge. These were used as informative priors in a Bayesian inference of the PoS variogram from BSO and implemented using a Markov chain Monte Carlo algorithm. ATP conditional simulation was done to obtain stochastic simulations at point support. MODIS (Moderate Resolution Imaging Spectroradiometer) atmospheric temperature profile data were used in an illustrative example. The outcomes from the Bayesian ATP inference for the Matérn variogram model parameters confirmed that the posterior distribution of the nugget parameter was effectively the same as its prior distribution; for the other parameters, the uncertainty was substantially decreased when BSO were introduced to the Bayesian ATP estimator. This confirmed that expert knowledge brought new information to infer the nugget effect at PoS while BSO only brought new information to infer the other parameters. Bayesian ATP conditional simulations provided a satisfactory way to quantify parameters and model uncertainty propagation through spatial disaggregation.     

非线性半参数模型最小二乘核估计法方程系数阵的非奇异性质

本文基于非线性半参数模型最小二乘核估计的迭代解法,证明了非线性半参数模型最小二乘类估计法方程系数阵在一定条件下的非奇异性。这种性质可类推到非线性半参数模型的其他最小二乘类估计方法和其他非线性解算方法,这是对非线性半参数模型估计理论的初步推导。     

A theoretical study on terrestrial gravimetric data refinement by Earth gravity models

The idea of this paper is to present estimators for combining terrestrial gravity data with Earth gravity models and produce a high‐quality source of the Earth's gravity field data through all wavelengths. To do so, integral and point‐wise estimators are mathematically developed, based on the spectral combination theory, in such a way that they combine terrestrial data with one and/or two Earth gravity models. The integral estimators are developed so that they become biased or unbiased to a priori information. For testing the quality of the estimators, their global mean square errors are generated using an Earth gravity model08 model and one of the recent products of the gravity field and steady‐state ocean circulation explorer mission. Numerical results show that the integral estimators have smaller global root mean square errors than the point‐wise ones but they are not efficient practically. The integral estimator of the biased type is the most suited due to its smallest global root mean square error comparing to the rest of the estimators. Due largely to the omission errors of Earth gravity models the point‐wise estimators are not sensitive to the Earth gravity model commission error; therefore, the use of high‐degree Earth gravity models is very influential for reduction of their root mean square errors. Also it is shown that the use of the ocean circulation explorer Earth gravity model does not significantly reduce the root mean square errors of the presented estimators in the presence of Earth gravity model08. All estimators are applied in the region of Fennoscandia and a cap size of 2° for numerical integration and a maximum degree of 2500 for generation of band‐limited kernels are found suitable for the integral estimators.