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首页> 外文期刊>Journal of Contemporary Mathematical Analysis >Asymptotic Behavior of the Variance of the Best Linear Unbiased Estimator for the Mean of a Discrete-time Singular Stationary Process
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Asymptotic Behavior of the Variance of the Best Linear Unbiased Estimator for the Mean of a Discrete-time Singular Stationary Process

机译：用于离散时间单数静止过程的最佳线性无偏估计差异的渐近行为

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摘要

It is known that for a wide class of discrete-time stationary processes possessing spectral densities f, the variance sigma n2(f) of the best linear unbiased estimator for the mean depends asymptotically only on the behavior of the spectral density f near the origin, and behaves hyperbolically as n - infinity. In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of sigma n2(f) as n - infinity. In particular, we show that a necessary condition for sigma n2(f) to decrease to zero exponentially is that the spectral density f vanishes on a set of positive measure in any vicinity of zero, and if f vanishes only at the origin, then it is impossible to obtain exponential decay of sigma n2(f), no mater how high the order of the zero of f at the origin.
机译：众所周知，对于具有光谱密度f的广泛的离散时间静止过程，对于平均值的最佳线性无偏估计器的方差Sigma N2（F）仅取决于诸如原点附近的光谱密度F的行为。并且以n - >无穷大而行为。在本文中，我们获得必要的以及σn2（f）作为n - >无穷大的指数速率的充分条件。特别地，我们表明Sigma N2（F）指数下降到零的必要条件是频谱密度F在零附近的一组正措施上消失，如果F仅在原点消失不可能获得Σ22（f）的指数衰减，没有母体如何在原点处的零的顺序高。

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