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次序统计量之差的鞍点近似AI 解读

Saddlepoint approximations for the distribution of the difference of order statistics from a continuous distribution are presented. The approximations are illustrated for the case of the exponential distribution where we can find the exact probability density function of the difference of order statistics, and for the case of the noncentral chi-squared distribution which has application to the problem of testing a time series for linearity. In both cases we show that the…

因果型空间自回归过程估计量的偏差AI 解读

We study the asymptotic distribution of Yule-Walker and least squares estimators for twodimensional causal autoregressive processes observed on a rectangular part of a lattice. An explicit expression for the asymptotic bias of Yule-Walker estimators is obtained. It is shown that this bias disappears if we use the so-called unbiased sample autocovariance function or least squares estimators.

因果型空间自回归过程估计量的偏差AI 解读

We study the asymptotic distribution of Yule-Walker and least squares estimators for twodimensional causal autoregressive processes observed on a rectangular part of a lattice. An explicit expression for the asymptotic bias of Yule-Walker estimators is obtained. It is shown that this bias disappears if we use the so-called unbiased sample autocovariance function or least squares estimators.

阶数估计对自回归谱密度峰值频率估计的影响AI 解读

The effect of estimating the order of an autoregressive process on estimating the peak frequency is examined. For consistent order determining methods it is shown that the asymptotic results are the same as for the case when the order is known. For the order criteria which asymptotically overestimate the order, the peak frequency estimator is shown to be a consistent estimator of the true peak frequency.

自回归谱的同时置信带AI 解读

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on the estimated spectral density. We propose and illustrate a method for determining asymptotic simultaneous confidence bands using Scheffé projections.

自回归谱的同时置信带AI 解读

A shortcoming in the use of autoregressive spectral estimation has been the lack of methods for placing confidence intervals or bands on the estimated spectral density. We propose and illustrate a method for determining asymptotic simultaneous confidence bands using Scheffé projections.

确定时间序列周期的一种方法AI 解读

The periods corresponding to peaks in the autoregressive and window spectral density estimators are shown to be consistent and asymptotically normal estimators of peak periods in the true spectral density under assumptions of known autoregressive order and under slight modifications of the assumptions often made to show the asymptotic normality of window estimators, respectively. The asymptotic variances are obtained, and the use of the theory is illustrated by obtaining an…

确定时间序列周期的一种方法AI 解读

The periods corresponding to peaks in the autoregressive and window spectral density estimators are shown to be consistent and asymptotically normal estimators of peak periods in the true spectral density under assumptions of known autoregressive order and under slight modifications of the assumptions often made to show the asymptotic normality of window estimators, respectively. The asymptotic variances are obtained, and the use of the theory is illustrated by obtaining an…