Asymptotics for linear approximations of smooth functions of means
A higher-order version of the linear approximation of smooth functions of means proposed in Pallini (2002) is defined and studied. This version is shown to improve over the error of order Op(n -2) in probability, as the sample size n diverges, yielding a smaller error of order Op(n -3), as n diverge...
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University of Bologna
2007-10-01
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| Series: | Statistica |
| Online Access: | http://rivista-statistica.unibo.it/article/view/62 |
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doaj-c4da708f309c48bb8fb87eea113d0ee42020-11-24T23:19:47ZengUniversity of BolognaStatistica0390-590X1973-22012007-10-0164462564110.6092/issn.1973-2201/6257Asymptotics for linear approximations of smooth functions of meansAndrea PalliniA higher-order version of the linear approximation of smooth functions of means proposed in Pallini (2002) is defined and studied. This version is shown to improve over the error of order Op(n -2) in probability, as the sample size n diverges, yielding a smaller error of order Op(n -3), as n diverges. Both linear approximations are shown to have a normal distribution, as diverges. Empirical results of a simulation study on the ratio of means example are presented.http://rivista-statistica.unibo.it/article/view/62 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Andrea Pallini |
| spellingShingle |
Andrea Pallini Asymptotics for linear approximations of smooth functions of means Statistica |
| author_facet |
Andrea Pallini |
| author_sort |
Andrea Pallini |
| title |
Asymptotics for linear approximations of smooth functions of means |
| title_short |
Asymptotics for linear approximations of smooth functions of means |
| title_full |
Asymptotics for linear approximations of smooth functions of means |
| title_fullStr |
Asymptotics for linear approximations of smooth functions of means |
| title_full_unstemmed |
Asymptotics for linear approximations of smooth functions of means |
| title_sort |
asymptotics for linear approximations of smooth functions of means |
| publisher |
University of Bologna |
| series |
Statistica |
| issn |
0390-590X 1973-2201 |
| publishDate |
2007-10-01 |
| description |
A higher-order version of the linear approximation of smooth functions of means proposed in Pallini (2002) is defined and studied. This version is shown to improve over the error of order Op(n -2) in probability, as the sample size n diverges, yielding a smaller error of order Op(n -3), as n diverges. Both linear approximations are shown to have a normal distribution, as diverges. Empirical results of a simulation study on the ratio of means example are presented. |
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http://rivista-statistica.unibo.it/article/view/62 |
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AT andreapallini asymptoticsforlinearapproximationsofsmoothfunctionsofmeans |
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