Abstract We analyze the properties of the Maximum Likelihood (ML) estimator when the underlying log-likelihood function is numerically maximized with the so-called zig-zag algorithm. By splitting the parameter vector into sub-vectors, the algorithm maximizes the log-likelihood function alternatingly with respect to one sub-vector while keeping the others constant. For situations when the algorithm is initialized with a consistent estimator and is iterated sufficiently often, we establish the asymptotic equivalence of the zig-zag estimator and the “infeasible” ML estimator being numerically approximated. This result gives guidance for practical implementations. We illustrate how to employ the algorithm in different estimation problems, such as in a vine copula model and a vector autoregressive moving average model. The accuracy of the estimator is illustrated through simulations. Finally, we demonstrate the usefulness of our results in an application, where the Bitcoin heating 2017 is analyzed by a dynamic conditional correlation model.

中文翻译：

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使用 Zig-Zag 算法的最大似然估计

摘要 我们分析了最大似然 (ML) 估计器的属性，当底层对数似然函数使用所谓的之字形算法在数值上最大化时。通过将参数向量拆分为子向量，该算法使对数似然函数相对于一个子向量交替最大化，同时保持其他子向量不变。对于使用一致估计量初始化算法并且迭代足够频繁的情况，我们建立了 zig-zag 估计量和数值逼近的“不可行”ML 估计量的渐近等价性。该结果为实际实施提供了指导。我们说明了如何在不同的估计问题中使用该算法，例如在 vine copula 模型和向量自回归移动平均模型中。通过仿真说明了估计器的准确性。最后，我们展示了我们的结果在应用程序中的有用性，其中通过动态条件相关模型分析了 2017 年比特币加热。