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约翰·W.图基在时间序列与谱分析方面的工作AI 解读

The contributions of John W. Tukey to time series analysis, particularly spectrum analysis, are reviewed and discussed. The contributions include: methods, their properties, terminology, popularization, philosophy, applications and education. Much of Tukey's early work on spectrum analysis remained unpublished for many years, but the 1959 book by Blackman and Tukey made his approach accessible to a wide audience. In 1965 the Cooley-Tukey paper on the Fast Fourier Transform…

平稳时间序列上叠加单调趋势的一致检测AI 解读

Consider a time series made up of a signal and a stationary autocorrelated error series. A statistic is proposed for examining the hypothesis that the signal term is constant versus the hypothesis that it is monotonic in time. The statistic is the ratio of a linear combination of the time series values, with coefficients introduced by Abelson & Tukey (1963), to an estimate of the standard error of the linear combination. The statistic has asymptotic power 1 for a broad class…

平稳时间序列上叠加单调趋势的一致检测AI 解读

Consider a time series made up of a signal and a stationary autocorrelated error series. A statistic is proposed for examining the hypothesis that the signal term is constant versus the hypothesis that it is monotonic in time. The statistic is the ratio of a linear combination of the time series values, with coefficients introduced by Abelson & Tukey (1963), to an estimate of the standard error of the linear combination. The statistic has asymptotic power 1 for a broad class…

地震学与神经生理学随机过程数据的若干统计方法AI 解读

Examples are presented of statistical techniques for the analysis of random process data and of their uses in the substantive fields of seismology and neurophysiology. The problems addressed include frequency estimation for decaying cosinusoids, signal estimation, association measurement, causal connection assessment, estimation of speed and direction and structural modeling. The techniques employed include complex demodulation, nonlinear regression, probit analysis,…

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一类特定非线性时间序列系统的识别AI 解读

A nonlinear time series system is considered. The system has the property that the output series corresponding to a given input series is the sum of a noise series and the result of applying in turn the operations of linear filtering, instantaneous functional composition and linear filtering to the input series. Given a stretch of Gaussian input series and corresponding output series, estimates are constructed of the transfer functions of the linear filters, up to constant…

一种特定非线性时间序列系统的识别AI 解读

A nonlinear time series system is considered. The system has the property that the output series corresponding to a given input series is the sum of a noise series and the result of applying in turn the operations of linear filtering, instantaneous functional composition and linear filtering to the input series. Given a stretch of Gaussian input series and corresponding output series, estimates are constructed of the transfer functions of the linear filters, up to constant…

二元平稳点过程二阶强度的估计AI 解读

Summary We consider histogram and smoothed histogram type estimates of the auto and cross intensity functions of a bivariate stationary point process. The asymptotic distributions are found to be multiples of Poissons in the histogram case and linear combinations of Poissons in the smoothed case. These asymptotic distributions suggest the plotting of the square roots of the estimates in order to stabilize the variance and to make the distributions more nearly normal. Two…

We find the asymptotic distribution of two statistics that have been employed in the search for periodicities. Both statistics are based on Buys-Ballot tables. The first, the Whittaker periodogram, is computed for ordinary time series. The second, a X2 statistic, is computed for point processes. These statistics have been viewed as competitors of power spectrum estimates. We find that when autocorrelation is present in the process involved, the large-sample distributions of…

平稳过程下Whittaker周期图及相关卡方统计量的渐近分布AI 解读

We find the asymptotic distribution of two statistics that have been employed in the search for periodicities. Both statistics are based on Buys-Ballot tables. The first, the Whittaker periodogram, is computed for ordinary time series. The second, a X2 statistic, is computed for point processes. These statistics have been viewed as competitors of power spectrum estimates. We find that when autocorrelation is present in the process involved, the large-sample distributions of…

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利用零点估计平稳二元高斯过程的互谱AI 解读

Summary Under regularity conditions the cross-spectrum of a stationary, bivariate, Gaussian process, continuous in mean and with unit variance, may be estimated consistently as T → ∞ from the zeros in the interval [0, T] of its two components and the knowledge that the components have the same or opposite sign at time 0. The power spectra of the components may be estimated from the respective components' zeros alone. The estimates are asymptotically normal and unbiased.…

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