AU - Wang, Nan
AU - Liu, Wei
TI - Second Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum
PT - JOURNAL ARTICLE
TA - JIRSS
JN - JIRSS
VO - 2
VI - 1
IP - 1
4099 - http://jirss.irstat.ir/article-1-95-en.html
4100 - http://jirss.irstat.ir/article-1-95-en.pdf
SO - JIRSS 1
AB - This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright} where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of random variables satifying certain assumptions. These moment expansions complement the classical central limit theorem for a random number of i.i.d. random variables when the random number has the form ta, which arises from many sequential statistical procedures. They can be used to correct higher order bias and/or skewness in S_{t_{a}}^{prime }/sqrt{t_{a}} to make asymptotic approximation more accurate for small and moderate sample sizes.
CP - IRAN
IN -
LG - eng
PB - JIRSS
PG - 115
PT -
YR - 2003