ON STRONG LAWS OF LARGE NUMBERS FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM ELEMENTS

ON STRONG LAWS OF LARGE NUMBERS FOR ARRAYS OF ROWWISE INDEPENDENT RANDOM ELEMENTS

Let {X_(nk)} be an array of rowwise independent random elements in a separable Banach space of type r, 1 ≤ r ≤ 2. Complete convergence of (The equation is abbreviated), 0 ＜ p ＜ r ≤ 2 is obtained when (The equation is abbreviated), α ≥ 0 with v(1/p-1/r) ＞ α+1. An application to density estimation is...

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Veröffentlicht in:International Journal of Mathematics and Mathematical Sciences 1993, Vol.1993 (3), p.587-591
Hauptverfasser: Bozorgnia, Abolghassem, Patterson, Ronald Frank, Taylor, Robert Lee
Format: Artikel
Sprache:eng
Schlagworte:
complete convergence
Rademacher r type space
radom element
strong laws of large number
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Zusammenfassung:Let {X_(nk)} be an array of rowwise independent random elements in a separable Banach space of type r, 1 ≤ r ≤ 2. Complete convergence of (The equation is abbreviated), 0 ＜ p ＜ r ≤ 2 is obtained when (The equation is abbreviated), α ≥ 0 with v(1/p-1/r) ＞ α+1. An application to density estimation is also given.
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171293000729