Asymptotic rate of convergence versus the “asymptotics” of any series expansion
On page 68 of Christopher Small's Expansions and Asymptotics for Statistics, we look at:
$$
E(T_n)=sqrt{frac{8}{pi n}}e^{-n/8}Big(1-frac{8}{n}+frac{96}{n^2}-cdotsBig).
$$
(Here, $n$ is the sample size and $T_n$ is a function of the observed data.)
The authors then write:
In this example, the asymptotic rate of convergence of $T_n$ to zero
is superexponential. However, the expansion is "$n$-asymptotic" in
nature.
(The boldfacing is mine.)
Up to the page cited above, the boldfaced terms above are not defined rigorously. What do they refer to and could you please recommend a more elementary text that deal with (topics that eventually lead to) those terms?
statistics reference-request asymptotics
asked Nov 18 at 16:14
yurnero
7,3651925
add a comment |
On page 68 of Christopher Small's Expansions and Asymptotics for Statistics, we look at:
$$
E(T_n)=sqrt{frac{8}{pi n}}e^{-n/8}Big(1-frac{8}{n}+frac{96}{n^2}-cdotsBig).
$$
(Here, $n$ is the sample size and $T_n$ is a function of the observed data.)
The authors then write:
In this example, the asymptotic rate of convergence of $T_n$ to zero
is superexponential. However, the expansion is "$n$-asymptotic" in
nature.
(The boldfacing is mine.)
Up to the page cited above, the boldfaced terms above are not defined rigorously. What do they refer to and could you please recommend a more elementary text that deal with (topics that eventually lead to) those terms?
statistics reference-request asymptotics
asked Nov 18 at 16:14
yurnero
7,3651925
Have you researched the literature to find the definitions of the terms of interest?
– Mark Viola
Nov 18 at 16:35
@MarkViola I googled but didn't see anything up to my liking and that was why I posted here, hoping to find them in one accessible source.
– yurnero
Nov 18 at 17:37
@MarkViola I also looked at the references cited at the end of the book chapter containing the quote above. They are: Spivak's Calculus, Witttake and Watson's A Course of Modern Analysis, and Wong's Asymptotic Approximations of Integrals.
– yurnero
Nov 18 at 17:46
add a comment |
On page 68 of Christopher Small's Expansions and Asymptotics for Statistics, we look at:
$$
E(T_n)=sqrt{frac{8}{pi n}}e^{-n/8}Big(1-frac{8}{n}+frac{96}{n^2}-cdotsBig).
$$
(Here, $n$ is the sample size and $T_n$ is a function of the observed data.)
The authors then write:
In this example, the asymptotic rate of convergence of $T_n$ to zero
is superexponential. However, the expansion is "$n$-asymptotic" in
nature.
(The boldfacing is mine.)
Up to the page cited above, the boldfaced terms above are not defined rigorously. What do they refer to and could you please recommend a more elementary text that deal with (topics that eventually lead to) those terms?
statistics reference-request asymptotics
asked Nov 18 at 16:14
yurnero
7,3651925
On page 68 of Christopher Small's Expansions and Asymptotics for Statistics, we look at:
$$
E(T_n)=sqrt{frac{8}{pi n}}e^{-n/8}Big(1-frac{8}{n}+frac{96}{n^2}-cdotsBig).
$$
(Here, $n$ is the sample size and $T_n$ is a function of the observed data.)
The authors then write:
In this example, the asymptotic rate of convergence of $T_n$ to zero
is superexponential. However, the expansion is "$n$-asymptotic" in
nature.
(The boldfacing is mine.)
Up to the page cited above, the boldfaced terms above are not defined rigorously. What do they refer to and could you please recommend a more elementary text that deal with (topics that eventually lead to) those terms?
statistics reference-request asymptotics
statistics reference-request asymptotics
asked Nov 18 at 16:14
yurnero
7,3651925
asked Nov 18 at 16:14
yurnero
7,3651925
asked Nov 18 at 16:14
yurnero
7,3651925
asked Nov 18 at 16:14
yurnero
7,3651925
asked Nov 18 at 16:14
yurnero
7,3651925
7,3651925
Have you researched the literature to find the definitions of the terms of interest?
– Mark Viola
Nov 18 at 16:35
@MarkViola I googled but didn't see anything up to my liking and that was why I posted here, hoping to find them in one accessible source.
– yurnero
Nov 18 at 17:37
@MarkViola I also looked at the references cited at the end of the book chapter containing the quote above. They are: Spivak's Calculus, Witttake and Watson's A Course of Modern Analysis, and Wong's Asymptotic Approximations of Integrals.
– yurnero
Nov 18 at 17:46
add a comment |
Have you researched the literature to find the definitions of the terms of interest?
– Mark Viola
Nov 18 at 16:35
@MarkViola I googled but didn't see anything up to my liking and that was why I posted here, hoping to find them in one accessible source.
– yurnero
Nov 18 at 17:37
@MarkViola I also looked at the references cited at the end of the book chapter containing the quote above. They are: Spivak's Calculus, Witttake and Watson's A Course of Modern Analysis, and Wong's Asymptotic Approximations of Integrals.
– yurnero
Nov 18 at 17:46
Have you researched the literature to find the definitions of the terms of interest?
– Mark Viola
Nov 18 at 16:35
Have you researched the literature to find the definitions of the terms of interest?
– Mark Viola
Nov 18 at 16:35
@MarkViola I googled but didn't see anything up to my liking and that was why I posted here, hoping to find them in one accessible source.
– yurnero
Nov 18 at 17:37
@MarkViola I googled but didn't see anything up to my liking and that was why I posted here, hoping to find them in one accessible source.
– yurnero
Nov 18 at 17:37
@MarkViola I also looked at the references cited at the end of the book chapter containing the quote above. They are: Spivak's Calculus, Witttake and Watson's A Course of Modern Analysis, and Wong's Asymptotic Approximations of Integrals.
– yurnero
Nov 18 at 17:46
@MarkViola I also looked at the references cited at the end of the book chapter containing the quote above. They are: Spivak's Calculus, Witttake and Watson's A Course of Modern Analysis, and Wong's Asymptotic Approximations of Integrals.
– yurnero
Nov 18 at 17:46
add a comment |
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Have you researched the literature to find the definitions of the terms of interest?
– Mark Viola
Nov 18 at 16:35
@MarkViola I googled but didn't see anything up to my liking and that was why I posted here, hoping to find them in one accessible source.
– yurnero
Nov 18 at 17:37
@MarkViola I also looked at the references cited at the end of the book chapter containing the quote above. They are: Spivak's Calculus, Witttake and Watson's A Course of Modern Analysis, and Wong's Asymptotic Approximations of Integrals.
– yurnero
Nov 18 at 17:46