کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1149324 | 957872 | 2010 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Coverage accuracy for a mean without third moment
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
For constructing a confidence interval for the mean of a random variable with a known variance, one may prefer the sample mean standardized by the true standard deviation to the Student's t-statistic since the information of knowing the variance is used in the former way. In this paper, by comparing the leading error term in the expansion of the coverage probability, we show that the above statement is not true when the third moment is infinite. Our theory prefers the Student's t-statistic either when one-sided confidence intervals are considered for a heavier tail distribution or when two-sided confidence intervals are considered. Unlike other existing expansions for the Student's t-statistic, the derived explicit expansion for the case of infinite third moment can be used to estimate the coverage error so that bias correction becomes possible.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Statistical Planning and Inference - Volume 140, Issue 4, April 2010, Pages 1082-1088
Journal: Journal of Statistical Planning and Inference - Volume 140, Issue 4, April 2010, Pages 1082-1088
نویسندگان
Yun Gong, Liang Peng,