Estimation of mean shift in a temporally ordered sequence of random variables with a possible existence of change-point is an important problem in many disciplines. In the available literature of more than fifty years the estimation methods of the mean shift is usually dealt as a two-step problem. A test for the existence of a change-point is followed by an estimation process of the mean shift, which is known as testimator. The problem suffers from over parametrization. When viewed as an estimation problem, we establish that the maximum likelihood estimator (MLE) always gives a false alarm indicting an existence of a change-point in the given sequence even though there is no change-point at all. After modelling the parameter space as a modified horn torus. We introduce a new method of estimation of the parameters. The newly introduced estimation method of the mean shift is assessed with a proper Riemannian metric on that conic manifold. It is seen that its performance is superior compared to that of the MLE. The proposed method is implemented on Bitcoin data and compared its performance with the performance of the MLE.

翻译：在具有潜在变点的时序随机变量序列中估计均值偏移是众多学科中的重要问题。在超过五十年的现有文献中，均值偏移的估计方法通常被处理为两步问题：首先进行变点存在性检验，随后进行均值偏移的估计过程（即检验估计量）。该问题存在过度参数化的缺陷。当将其视为估计问题时，我们证明最大似然估计量（MLE）总会产生虚假警报——即使在序列根本不存在变点的情况下，仍会指示变点的存在。通过将参数空间建模为修正的喇叭环面，我们引入了一种新的参数估计方法。这种新提出的均值偏移估计方法通过在该圆锥流形上定义适当的黎曼度量进行评估。结果表明，其性能显著优于最大似然估计量。我们将所提方法应用于比特币数据，并将其性能与最大似然估计量进行了对比分析。