On the asymptotic of likelihood ratios for self-normalized large deviations
| dc.creator | Chi, Zhiyi | |
| dc.date | 2007-09-10 | |
| dc.date | 2008-01-30 | |
| dc.date.accessioned | 2026-07-07T08:56:58Z | |
| dc.date.available | 2026-07-07T08:56:58Z | |
| dc.description | Motivated by multiple statistical hypothesis testing, we obtain the limit of likelihood ratio of large deviations for self-normalized random variables, specifically, the ratio of $P(\sqrt{n}(\bar X +d/n) \ge x_n V)$ to $P(\sqrt{n}\bar X \ge x_n V)$, as $n\toi$, where $\bar X$ and $V$ are the sample mean and standard deviation of iid $X_1, ..., X_n$, respectively, $d>0$ is a constant and $x_n \toi$. We show that the limit can have a simple form $e^{d/z_0}$, where $z_0$ is the unique maximizer of $z f(x)$ with $f$ the density of $X_i$. The result is applied to derive the minimum sample size per test in order to control the error rate of multiple testing at a target level, when real signals are different from noise signals only by a small shift. | |
| dc.description | typos on pages 1, 3 and 8 of the same type: missing or extra \sqrt{n} in the expressions of probabilities of large deviations | |
| dc.identifier | https://arxiv.org/abs/0709.1506 | |
| dc.identifier | http://arxiv.org/abs/0709.1506 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146803 | |
| dc.subject | Statistics Theory | |
| dc.subject | Probability | |
| dc.subject | 60F10 (Primary); 62H15 (Secondary) | |
| dc.title | On the asymptotic of likelihood ratios for self-normalized large deviations | |
| dc.type | text |