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- W4301737665 abstract "The Marcinkiewicz Strong Law, $displaystylelim_{ntoinfty}frac{1}{n^{frac1p}}sum_{k=1}^n (D_{k}- D)=0$ a.s. with $pin(1,2)$, is studied for outer products $D_k=X_koverline{X}_k^T$, where ${X_k},{overline{X}_k}$ are both two-sided (multivariate) linear processes ( with coefficient matrices $(C_l), (overline{C}_l)$ and i.i.d. zero-mean innovations ${Xi}$, ${overline{Xi}}$). Matrix sequences $C_l$ and $overline{C}_l$ can decay slowly enough (as $|l|toinfty$) that ${X_k,overline{X}_k}$ have long-range dependence while ${D_k}$ can have heavy tails. In particular, the heavy-tail and long-range-dependence phenomena for ${D_k}$ are handled simultaneously and a new decoupling property is proved that shows the convergence rate is determined by the worst of the heavy-tails or the long-range dependence, but not the combination. The main result is applied to obtain Marcinkiewicz Strong Law of Large Numbers for stochastic approximation, non-linear functions forms and autocovariances." @default.
- W4301737665 created "2022-10-05" @default.
- W4301737665 creator A5040554923 @default.
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- W4301737665 date "2015-01-10" @default.
- W4301737665 modified "2023-10-14" @default.
- W4301737665 title "Marcinkiewicz Law of Large Numbers for Outer-products of Heavy-tailed, Long-range Dependent Data" @default.
- W4301737665 doi "https://doi.org/10.48550/arxiv.1501.02415" @default.
- W4301737665 hasPublicationYear "2015" @default.
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