Strong consistencies of the bootstrap moments
Let X be a real valued random variable with E|X|r+δ<∞ for some positive integer r and real number, δ, 0<δ≤r, and let {X,X1,X2,…} be a sequence of independent, identically distributed random variables. In this note, we prove that, for almost all w∈Ω, μr;n*(w)→μr with probability 1. if limn→∞i...
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| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291001060 |
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| _version_ | 1849691549076553728 |
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| author | Tien-Chung Hu |
| author_facet | Tien-Chung Hu |
| author_sort | Tien-Chung Hu |
| collection | DOAJ |
| description | Let X be a real valued random variable with E|X|r+δ<∞ for some positive
integer r and real number, δ, 0<δ≤r, and let {X,X1,X2,…} be a sequence of
independent, identically distributed random variables. In this note, we prove that,
for almost all w∈Ω, μr;n*(w)→μr with probability 1. if limn→∞infm(n)n−β>0 for
some β>r−δr+δ, where μr;n* is the bootstrap rth sample moment of the bootstrap sample some
with sample size m(n) from the data set {X,X1,…,Xn} and μr is the rth moment of
X. The results obtained here not only improve on those of Athreya [3] but also the
proof is more elementary. |
| format | Article |
| id | doaj-art-e1b491fc1b5c4c3e8269fe1250d1c413 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e1b491fc1b5c4c3e8269fe1250d1c4132025-08-20T03:20:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114479780210.1155/S0161171291001060Strong consistencies of the bootstrap momentsTien-Chung Hu0Department of Mathematics, National Tsing Hua University, Hsinchu 3004, TaiwanLet X be a real valued random variable with E|X|r+δ<∞ for some positive integer r and real number, δ, 0<δ≤r, and let {X,X1,X2,…} be a sequence of independent, identically distributed random variables. In this note, we prove that, for almost all w∈Ω, μr;n*(w)→μr with probability 1. if limn→∞infm(n)n−β>0 for some β>r−δr+δ, where μr;n* is the bootstrap rth sample moment of the bootstrap sample some with sample size m(n) from the data set {X,X1,…,Xn} and μr is the rth moment of X. The results obtained here not only improve on those of Athreya [3] but also the proof is more elementary.http://dx.doi.org/10.1155/S0161171291001060bootstrap sample sizesample momentconvergence with probability 1. |
| spellingShingle | Tien-Chung Hu Strong consistencies of the bootstrap moments International Journal of Mathematics and Mathematical Sciences bootstrap sample size sample moment convergence with probability 1. |
| title | Strong consistencies of the bootstrap moments |
| title_full | Strong consistencies of the bootstrap moments |
| title_fullStr | Strong consistencies of the bootstrap moments |
| title_full_unstemmed | Strong consistencies of the bootstrap moments |
| title_short | Strong consistencies of the bootstrap moments |
| title_sort | strong consistencies of the bootstrap moments |
| topic | bootstrap sample size sample moment convergence with probability 1. |
| url | http://dx.doi.org/10.1155/S0161171291001060 |
| work_keys_str_mv | AT tienchunghu strongconsistenciesofthebootstrapmoments |