| Autor: |
Butucea, Cristina, Meister, Alexander, Rohde, Angelika |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be well-approximable in a linear space of lower dimension $K_n$ with eigenvalues uniformly bounded away from zero and infinity. We prove asymptotic equivalence of this experiment and a class of $K_n$-dimensional Gaussian models with informative expectation in Le Cam's sense when $n$ tends to infinity and $K_n$ is allowed to increase moderately in $n$ at a polynomial rate. For this purpose we derive a new localization technique for non-i.i.d. data and a novel high-dimensional Central Limit Law in total variation distance. These results are key ingredients to show asymptotic equivalence between the experiments of locally stationary Gaussian time series and a bivariate Wiener process with the log spectral density as its drift. Therein a novel class of matrices is introduced which generalizes circulant Toeplitz matrices traditionally used for strictly stationary time series. |
| Databáze: |
arXiv |
| Externí odkaz: |
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