采样问题在最小二乘,傅里叶分析,和数论方法在参数估计

S. Casey
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引用次数: 2

摘要

给定满足一定条件的周期点过程的噪声数据,最小二乘程序可用于求解周期的最大似然估计。在更一般的条件下,傅立叶分析方法,例如维纳周期图,可以用来求解近似最大似然的估计。然而,当数据中缺失的观测值越来越多时,这些方法就失效了。与这些方法并列,数论方法提供了参数估计,虽然不是最大似然,但可以用作初始化算法,达到中等噪声水平的Cramer-Rao界。我们描述了最小二乘程序和傅立叶分析方法不能产生接近最大似然估计的条件,并表明数论方法在这些情况下提供了可靠的估计。我们还讨论了数论方法不能产生良好估计的数据类型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sampling issues in least squares, Fourier analytic, and number theoretic methods in parameter estimation
Given, noisy data from a periodic point process that satisfies certain conditions, least squares procedures can be used to solve for maximum likelihood estimates of the period. Under more general conditions, Fourier analytic methods, e.g., Wiener's periodogram, can be used to solve for estimates which are approximately maximum likelihood. However, these methods break down when the data has increasing numbers of missing observations. Juxtaposed with these methods, number theoretic methods provide parameter estimations that, while not being maximum likelihood, can be used as initialization in an algorithm that achieves the Cramer-Rao bound for moderate noise levels. We describe the conditions under which the least squares procedures and Fourier analytic methods do not produce estimates close to maximum likelihood, and show that the number theoretic methods provide a reliable estimate in these cases. We also discuss the type of data for which the number theoretic methods fail to produce good estimates.
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