| Title | On the lengths of t-based confidence intervals |
| Authors | Zhang, Yu Fang, Xiangzhong |
| Affiliation | Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China |
| Issue Date | Apr-2020 |
| Publisher | JOURNAL OF APPLIED STATISTICS |
| Abstract | Confidence interval is a basic type of interval estimation in statistics. When dealing with samples from a normal population with the unknown mean and the variance, the traditional method to construct t-based confidence intervals for the mean parameter is to treat the n sampled units as n groups and build the intervals. Here we propose a generalized method. We first divide them into several equal-sized groups and then calculate the confidence intervals with the mean values of these groups. If we define "better" in terms of the expected length of the confidence interval, then the first method is better because the expected length of the confidence interval obtained from the first method is shorter. We prove this intuition theoretically. We also specify when the elements in each group are correlated, the first method is invalid, while the second can give us correct results in terms of the coverage probability. We illustrate this with analytical expressions. In practice, when the data set is extremely large and distributed in several data centers, the second method is a good tool to get confidence intervals, in both independent and correlated cases. Some simulations and real data analyses are presented to verify our theoretical results. |
| URI | http://hdl.handle.net/20.500.11897/606694 |
| ISSN | 0266-4763 |
| DOI | 10.1080/02664763.2020.1754357 |
| Indexed | SCI(E) Scopus |
| Appears in Collections: | 数学科学学院 |
