Asymptotic behavior of the variance of the BLUE for the mean of stationary processes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915944810414080 |
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| author | Ginovyan, Mamikon S. |
| author_facet | Ginovyan, Mamikon S. |
| contents | In this paper, we survey results on the asymptotic behavior of the variance of the best linear unbiased estimator (BLUE) for the mean of stationary processes. This behavior is influenced by the regularity and memory structures of the observed models. The results show that the asymptotic behavior of the variance of the BLUE is determined solely by the behavior of the spectrum near the origin. For nondeterministic models, the variance of the BLUE exhibits hyperbolic behavior, similar to the power function, while for purely deterministic models, the variance decreases at an exponential rate. Specifically, a necessary condition for the variance of the BLUE to approach zero exponentially is that the spectral density of the model vanishes on a set of positive Lebesgue measure in any neighborhood of zero. We also present results on the asymptotic efficiency of various unbiased linear estimators in comparison to the BLUE. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_17705 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of the variance of the BLUE for the mean of stationary processes Ginovyan, Mamikon S. Statistics Theory Primary: 62F10, 62F12, 60G10, secondary: 62M15, 60G12 In this paper, we survey results on the asymptotic behavior of the variance of the best linear unbiased estimator (BLUE) for the mean of stationary processes. This behavior is influenced by the regularity and memory structures of the observed models. The results show that the asymptotic behavior of the variance of the BLUE is determined solely by the behavior of the spectrum near the origin. For nondeterministic models, the variance of the BLUE exhibits hyperbolic behavior, similar to the power function, while for purely deterministic models, the variance decreases at an exponential rate. Specifically, a necessary condition for the variance of the BLUE to approach zero exponentially is that the spectral density of the model vanishes on a set of positive Lebesgue measure in any neighborhood of zero. We also present results on the asymptotic efficiency of various unbiased linear estimators in comparison to the BLUE. |
| title | Asymptotic behavior of the variance of the BLUE for the mean of stationary processes |
| topic | Statistics Theory Primary: 62F10, 62F12, 60G10, secondary: 62M15, 60G12 |
| url | https://arxiv.org/abs/2604.17705 |