Araştırma Makalesi
Yıl 2018,
Cilt: 11 Sayı: 3, 46 - 52, 31.12.2018
Öz
We derive strong laws of large numbers for combinatorial sums iXniπn(i), where Xnij are n × n matrices of random variables with finite fourth moments and (πn(1), . . . , πn(n)) are uniformly distributed random permutations of 1, . . . , n independent with X’s. We do not assume the independence of X’s, but this case is included as well. Examples are discussed.
Anahtar Kelimeler
Combinatorial central limit theorem combinatorial sums strong law of large numbers
Kaynakça
- von Bahr B. (1976). Remainder term estimate in a combinatorial central limit theorem, Z. Wahrsch. verw. Geb., 35, 131-139.
- Ho S.T., Chen L.H.Y. (1978). An Lp bounds for the remainder in a combinatorial central limit theorem, Ann. Probab., 6, 231-249.
- Bolthausen E. (1984). An estimate of the remainder in a combinatorial central limit theorem, Z. Wahrsch. verw. Geb., 66, 379-386.
- Goldstein L. (2005). Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing, J. Appl. Probab., 42, 661-683.
- Neammanee K., Suntornchost J. (2005). A uniform bound on a combinatorial central limit theorem, Stoch. Anal. Appl., 3, 559-578.
- Neammanee K., Rattanawong P. (2009). A constant on a uniform bound of a combinatorial central limit theorem, J. Math. Research, 1, 91-103.
- Chen L.H.Y., Fang X. (2015). 0n the error bound in a combinatorial central limit theorem, Bernoulli, 21 (1), 335-359.
- Frolov A.N. (2014). Esseen type bounds of the remainder in a combinatorial CLT, J. Statist. Planning and Inference, 149, 90-97.
- Frolov A.N. (2015a) Bounds of the remainder in a combinatorial central limit theorem, Statist. Probab. Letters, 105, 37-46.
- Frolov A.N. (2015b). On the probabilities of moderate deviations for combinatorial sums. Vestnik St. Petersburg University. Mathematics, 48(1), 23-28. Allerton Press, Inc., 2015.
- Frolov A.N. (2017). On Esseen type inequalities for combinatorial random sums. Communications in Statistics -Theory and Methods, 46(12), 5932-5940.
Yıl 2018,
Cilt: 11 Sayı: 3, 46 - 52, 31.12.2018
Öz
Kaynakça
- von Bahr B. (1976). Remainder term estimate in a combinatorial central limit theorem, Z. Wahrsch. verw. Geb., 35, 131-139.
- Ho S.T., Chen L.H.Y. (1978). An Lp bounds for the remainder in a combinatorial central limit theorem, Ann. Probab., 6, 231-249.
- Bolthausen E. (1984). An estimate of the remainder in a combinatorial central limit theorem, Z. Wahrsch. verw. Geb., 66, 379-386.
- Goldstein L. (2005). Berry-Esseen bounds for combinatorial central limit theorems and pattern occurrences, using zero and size biasing, J. Appl. Probab., 42, 661-683.
- Neammanee K., Suntornchost J. (2005). A uniform bound on a combinatorial central limit theorem, Stoch. Anal. Appl., 3, 559-578.
- Neammanee K., Rattanawong P. (2009). A constant on a uniform bound of a combinatorial central limit theorem, J. Math. Research, 1, 91-103.
- Chen L.H.Y., Fang X. (2015). 0n the error bound in a combinatorial central limit theorem, Bernoulli, 21 (1), 335-359.
- Frolov A.N. (2014). Esseen type bounds of the remainder in a combinatorial CLT, J. Statist. Planning and Inference, 149, 90-97.
- Frolov A.N. (2015a) Bounds of the remainder in a combinatorial central limit theorem, Statist. Probab. Letters, 105, 37-46.
- Frolov A.N. (2015b). On the probabilities of moderate deviations for combinatorial sums. Vestnik St. Petersburg University. Mathematics, 48(1), 23-28. Allerton Press, Inc., 2015.
- Frolov A.N. (2017). On Esseen type inequalities for combinatorial random sums. Communications in Statistics -Theory and Methods, 46(12), 5932-5940.
Toplam 11 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2018 |
| Kabul Tarihi | 15 Kasım 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 11 Sayı: 3 |
