Strong law of large numbers with operator normalizations for martingales and sums of orthogonal random vectors (Q2722137)
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scientific article; zbMATH DE number 1617381
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strong law of large numbers with operator normalizations for martingales and sums of orthogonal random vectors |
scientific article; zbMATH DE number 1617381 |
Statements
11 July 2001
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strong law of large numbers
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martingales
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sums of orthogonal random vectors
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operator normings
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linear regression
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autoregressive process
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strong consistency
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0.9341389
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0.9335992
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Strong law of large numbers with operator normalizations for martingales and sums of orthogonal random vectors (English)
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Necessary and sufficient conditions (Prokhorov-Loev-type) for strong LLN with operator normings for vector martingales and sequence sums of orthogonal random vectors are studied. Applications of the obtained general results are used to prove the strong consistency of least squares estimates of unknown coefficients in multi-dimensional linear regression and asymptotical properties of solutions of multi-dimensional stochastic recurrent equations.
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