An edgeworth expansion for a sum of M-Dependent random variables
Given a sequence X1,X2,…,Xn of m-dependent random variables with moments of order 3+α (0<α≦1), we give an Edgeworth expansion of the distribution of Sσ−1(S=X1+X2+…+Xn, σ2=ES2) under the assumption that E[exp(it Sσ1)] is small away from the origin. The result is of the best possible order....
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000618 |
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| _version_ | 1832563333240193024 |
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| author | Wan Soo Rhee |
| author_facet | Wan Soo Rhee |
| author_sort | Wan Soo Rhee |
| collection | DOAJ |
| description | Given a sequence X1,X2,…,Xn of m-dependent random variables with moments of order 3+α (0<α≦1), we give an Edgeworth expansion of the distribution of Sσ−1(S=X1+X2+…+Xn, σ2=ES2) under the assumption that E[exp(it Sσ1)] is small away from the origin. The result is of the best possible order. |
| format | Article |
| id | doaj-art-00dfff1cf5234ea68d5c47ba44f79ccc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-00dfff1cf5234ea68d5c47ba44f79ccc2025-02-03T01:20:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018356356910.1155/S0161171285000618An edgeworth expansion for a sum of M-Dependent random variablesWan Soo Rhee0Faculty of Management Sciences, The Ohio State University, Columbus 43210, Ohio, USAGiven a sequence X1,X2,…,Xn of m-dependent random variables with moments of order 3+α (0<α≦1), we give an Edgeworth expansion of the distribution of Sσ−1(S=X1+X2+…+Xn, σ2=ES2) under the assumption that E[exp(it Sσ1)] is small away from the origin. The result is of the best possible order.http://dx.doi.org/10.1155/S0161171285000618Edgeworth expansionm-dependentBerry-Esseen boundCentral limit theorem. |
| spellingShingle | Wan Soo Rhee An edgeworth expansion for a sum of M-Dependent random variables International Journal of Mathematics and Mathematical Sciences Edgeworth expansion m-dependent Berry-Esseen bound Central limit theorem. |
| title | An edgeworth expansion for a sum of M-Dependent random variables |
| title_full | An edgeworth expansion for a sum of M-Dependent random variables |
| title_fullStr | An edgeworth expansion for a sum of M-Dependent random variables |
| title_full_unstemmed | An edgeworth expansion for a sum of M-Dependent random variables |
| title_short | An edgeworth expansion for a sum of M-Dependent random variables |
| title_sort | edgeworth expansion for a sum of m dependent random variables |
| topic | Edgeworth expansion m-dependent Berry-Esseen bound Central limit theorem. |
| url | http://dx.doi.org/10.1155/S0161171285000618 |
| work_keys_str_mv | AT wansoorhee anedgeworthexpansionforasumofmdependentrandomvariables AT wansoorhee edgeworthexpansionforasumofmdependentrandomvariables |