In this paper, we obtain necessary as well as sufficient conditions for exponential rate of decrease of the variance of the best linear unbiased estimator (BLUE) for the unknown mean of a stationary sequence possessing a spectral density. In particular, we show that a necessary condition for variance of BLUE to decrease to zero exponentially is that the spectral density vanishes on a set of positive Lebesgue measure in any vicinity of zero.
Adenstedt, R. K., On large-sample estimation for the mean of a stationary random sequence, Ann. Stat., 2 (1974), 1095–1107.
Adenstedt, R. K., On large-sample estimation for the mean of a stationary random sequence, Ann. Stat., 2 (1974), 1095–1107.)| false
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Studia Scientiarum Mathematicarum Hungarica
2021 Volume 58
Magyar Tudományos Akadémia
H-1051 Budapest, Hungary, Széchenyi István tér 9.
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