Accuracy measures for parameter estimates represent a tricky issue in nonlinear models. Practitioners often use separate marginal confidence intervals for each parameter in place of a simultaneous confidence region (sCR). However, this can be extremely misleading due to the curvature of the parameter space of the nonlinear model. For low parameter dimensions, routines for evaluating approximate sCRs are available in the most common software programs; however, the degree of accuracy depends on the curvature of the parameter space and the sample size. Exact sCRs are computationally intensive, and for this reason, in the past, they did not receive much attention. In this paper, we perform a comparison among exact, asymptotic exact, approximate sCRs, and marginal confidence intervals. More modern regions based on bootstrap are also examined as an alternative approach (both parametric and nonparametric). Their degree of accuracy is compared with both real data and simulation results. Among the nonlinear models, in this paper, the focus is on two of the most widespread diffusion models of products and technologies, that is, the Bass and Generalized Bass models. Three different empirical studies are analyzed here. Simulation studies are also performed for lifecycles with the same diffusion characteristics as those of the empirical studies. Our results show that, as the parameter dimension increases, overlapping among the alternative sCRs reduces. The approximate sCR shows inadequate values of overlapping with the exact sCR, even for moderate parameter dimension. Bootstrap regions also exhibit good performance in describing the shape of the exact region when curvature is present, but they fail to spread up to its boundary. The coverage probability of each region is assessed with simulations. We observe that the coverage probability of the approximate sCR decreases rapidly, even for moderate parameter dimension, and it is smaller than the nominal level for bootstrap regions.

参数估计的精度度量是非线性模型中的一个棘手问题。从业者经常为每个参数使用单独的边际置信区间，以代替同时置信区域（sCR）。但是，由于非线性模型的参数空间的曲率，这可能会极具误导性。对于低参数尺寸，最常见的软件程序中提供了评估近似sCR的例程。但是，准确度取决于参数空间的曲率和样本大小。精确sCR是计算密集型的，因此，在过去，它们并没有受到太多关注。在本文中，我们对精确，渐近精确，近似sCR和边际置信区间进行了比较。还研究了基于引导的更现代区域作为替代方法（参数化和非参数化）。将其准确性与实际数据和仿真结果进行比较。在非线性模型中，本文重点关注产品和技术的两种最广泛的扩散模型，即Bass模型和Generalized Bass模型。这里分析了三种不同的实证研究。还对具有与经验研究相同的扩散特性的生命周期进行了模拟研究。我们的结果表明，随着参数维数的增加，备用sCR之间的重叠减少了。即使对于中等参数尺寸，近似sCR仍显示与精确sCR重叠的值不足。当存在曲率时，自举区域在描述精确区域的形状方面也表现出良好的性能，但是它们无法扩展到其边界。通过模拟评估每个区域的覆盖概率。我们观察到，即使对于中等参数尺寸，近似sCR的覆盖率也会迅速降低，并且小于引导区域的标称水平。当存在曲率时，自举区域在描述精确区域的形状方面也表现出良好的性能，但无法扩展到其边界。通过模拟评估每个区域的覆盖概率。我们观察到，即使对于中等参数尺寸，近似sCR的覆盖率也会迅速降低，并且小于引导区域的标称水平。当存在曲率时，自举区域在描述精确区域的形状方面也表现出良好的性能，但是它们无法扩展到其边界。通过模拟评估每个区域的覆盖概率。我们观察到，即使对于中等参数尺寸，近似sCR的覆盖率也会迅速降低，并且小于引导区域的标称水平。