On stability of trimmed sums

• Autorzy: Hu T.-C. , Huang C.-Y. , Rosalsky A.
• Języki publikacji: EN

Abstrakty

EN

Let {X_n, n ≥ 1} be a sequence of i.i.d. random variables and let {a_n, n ≥ 1} and {b_n, n ≥ 1} be sequences of constants where 0 < b_n ↑ ∞. Let X_n⁽¹⁾, X_n⁽²⁾,…, X_n⁽ⁿ⁾ be a rearrangement of X₁,…, X_n such that |X_n⁽¹⁾| ≥ |X_n⁽²⁾| ≥ … ≥ |X_n⁽ⁿ⁾|. Consider the sequence of weighted sums T_n = Σⁿ_i=1 a_i X_i, n ≥ 1, and, for fixed r ≥ 1, set T^(r)_n = Σⁿ_i=1 a_i X_i I(|X_i| ≤ |X^(r+1)_n|), n ≥ r + 1; i.e., T^(r)_n is the sum T_n minus the sum of the X^(k)_n’s multiplied by their corresponding coefficients for k = 1,…, r. The main results provide sufficient and, separately, necessary conditions for b⁻¹_n T^(r)_n − k_n → 0 almost surely for some sequence of centering constans {k_n, n ≥1}. The current work extends that of Mori [14], [15] wherein a_n ≡ 1.

Słowa kluczowe

EN

extreme terms; lightly trimmed sums; almost sure convergence; strong law of large numbers

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2003
• Tom: Vol. 23, Fasc. 1
• Strony: 153--172
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Hu T.-C.

• Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 300, R.O.C.

autor

Huang C.-Y.

• Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 300, R.O.C.

autor

Rosalsky A.

• Department of Statistics, University of Florida, Gainesville, Florida 32611, U.S.A.

Bibliografia

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