We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective probability distributions, and is to be classified as a minimum distance estimator, incorporating as a distance function the L^q-norm. Throughout, we deal rigorously with issues of existence and measurability of these implicitly defined estimators. Moreover, we provide consistency results in a common asymptotic setting, and compare our new method with classical estimators for the exponential, the Rayleigh and the Burr Type XII distribution in Monte Carlo simulation studies. We also assess the performance of different estimators for non-normalized models in the context of an exponential-polynomial family.

中文翻译：

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非标准化参数模型的最小 Lq 距离估计量

我们提出并研究了一种新的估计方法，用于由正半轴上的平滑密度函数组成的模型参数。该过程基于最近引入的各个概率分布的表征结果，并将被归类为最小距离估计器，将L ^q合并为距离函数-规范。在整个过程中，我们严格处理这些隐含定义的估计量的存在性和可测量性问题。此外，我们在常见的渐近设置中提供一致性结果，并将我们的新方法与蒙特卡罗模拟研究中的指数、瑞利和 Burr Type XII 分布的经典估计器进行比较。我们还在指数多项式族的背景下评估了非标准化模型的不同估计器的性能。