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时空协方差函数性质的非参数检验AI 解读

We propose a unified framework for testing various assumptions commonly made for covariance functions of stationary spatio-temporal random fields. The methodology is based on the asymptotic normality of space–time covariance estimators. We focus on tests for full symmetry and separability in this article, but our framework naturally covers testing for isotropy and Taylor's hypothesis. Our test successfully detects the asymmetric and nonseparable features in two sets of wind…

平稳空间点过程的最小二乘拟合AI 解读

Summary The K-function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K-function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through…

利用子抽样进行空间各向同性的非参数检验AI 解读

A common requirement for spatial modeling is the development of an appropriate correlation structure. Although the assumption of isotropy is often made for this structure, it is not always appropriate. A conventional practice when checking for isotropy is to informally assess plots of direction-specific sample (semi)variograms. Although a useful diagnostic, these graphical techniques are difficult to assess and open to interpretation. Formal alternatives to graphical…

标记点过程统计量的矩估计AI 解读

Summary In spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and we establish their L 2-consistency. The variance estimator in particular can be used for the construction of confidence intervals for estimated…

回归中的子序列方法AI 解读

We extend subseries methods for stationary sequences to the regression setting. To estimate sampling distributions, the subseries approach computes the statistic of interest on all possible subseries of a shorter length than the original series, and uses the distribution of these replicates to mimic the distribution of the original statistic. For proper choice of subseries length, the regression parameters can be estimated to order O(n -2/3), thus improving on the normal…

空间格点数据统计量的方差估计AI 解读

SUMMARY A statistic s() is computed on spatially indexed data {X i: i ∈ D), where D is a finite subset of the integer lattice Z2. We propose a method for estimating the variance (and other moments) of s() by using only the data. The set D may be irregularly shaped, the statistic s() may be arbitrarily complicated and no distributional assumptions (marginal or joint) are necessary. The method uses the statistic computed on overlapping 'subshapes' of D as replicates of s().…

重复样本直方图AI 解读

The “replicate histogram” is introduced as a simple diagnostic tool for describing the sampling distribution of a general statistic. It can be applied to virtually any statistic that has an asymptotic distribution, and the data on which the statistic is computed may be serially or spatially dependent. The method is completely sample based, requiring no theoretical analysis by the user, no knowledge of the proper standardization for the statistic, and no specification of the…

空间数据一般统计量矩的非参数估计AI 解读

A statistic s(·) is computed on spatially indexed data {X i : i ∈ D}, where D is a finite subset of the integer lattice Z2. We propose a simple nonparametric method for estimating the moments (e.g., variance, skewness) of s(D), using only the observed data at hand. The method uses “replicates” of s(·) computed on smaller subsets of D. No explicit knowledge of the underlying spatial dependence mechanism is needed, and the marginal distribution of X i may also be unknown. The…