The estimation of parameter standard errors for semi-variogram models is challenging, given the two-step process required to fit a parametric model to spatially correlated data. Motivated by an application in the social-epidemiology, we focus on exponential semi-variogram models fitted to data between 500 to 2000 observations and little control over the sampling design. Previously proposed methods for the estimation of standard errors cannot be applied in this context. Approximate closed form solutions are too costly using generalized least squares in terms of memory capacities. The generalized bootstrap proposed by Olea and Pardo-Ig\'uzquiza is nonetheless applicable with weighted instead of generalized least squares. However, the standard error estimates are hugely biased and imprecise. Therefore, we propose a filtering method added to the generalized bootstrap. The new development is presented and evaluated with a simulation study which shows that the generalized bootstrap with check-based filtering leads to massively improved results compared to the quantile-based filter method and previously developed approaches. We provide a case study using birthweight data.

翻译：半变异函数模型参数标准误的估计颇具挑战性，因为需要两步过程将参数模型拟合至空间相关数据。受社会流行病学应用启发，我们聚焦于拟合观测数在500至2000之间且采样设计可控性较低的指数半变异函数模型。此前提出的标准误估计方法在此背景下无法适用。采用广义最小二乘法求解近似封闭形式时，内存需求过高。Olea与Pardo-Igúzquiza提出的广义自助法虽可采用加权最小二乘法替代广义最小二乘法，但标准误估计存在严重偏差且精度不足。为此，我们提出一种在广义自助法中附加滤波的方法。通过仿真研究评估该新方法，结果表明基于检验滤波的广义自助法相较于基于分位数滤波的方法及此前提出的方法具有显著改进。我们以出生体重数据为例进行了案例研究。