Abstract
Suppose that the ℝd-valued random vector 0 is strictly operator-stable in the sense that μ̂, the characteristic function of 0, satisfies μ̂(z)t = μ̂(tB*z) for every t > 0, for some invertible linear operator B on ℝd. Suppose also that for the i.i.d. random vectors {Xi} in ℝd, n-B Σi=1n Xi→w 0. In the present paper, we study the rates of convergence of this operator-stable limit theorem in terms of several probability metrics. A new type of "ideal" metrics suitable for this rate-of-convergence problem is introduced.
Original language | English |
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Pages (from-to) | 37-85 |
Number of pages | 49 |
Journal | Journal of Theoretical Probability |
Volume | 9 |
Issue number | 1 |
DOIs | |
State | Published - Jan 1996 |
Keywords
- Operator-stable distributions
- Probability metrics
- Rate of convergence