Segmentation and estimation of change-point models: false positive control and confidence regions. (English) Zbl 1451.62035
Segmentation and estimation methods of change-point models are known to detect multiple change-points with high statistical accuracy. The goal of segmentation is to obtain those intervals in which the sequences behave as approximately stationary.
In this paper, the authors consider the following problem. Let \(X_{1},X_{2},\dots,X_{m}\) be independent and normally distributed with variances equal 1. Let us assume that there is \(M\ge 0\) and integers \(0=\tau_{0}<\tau_{1}<\cdots<\tau_{M}<\tau_{M+1}=m\) such that the mean \(\mu_{i}\) of \(X_{i}\), \(1\le i\le m\), is a step function with constant values on each of intervals \(\left(\tau_{k-1},\tau_{k} \right]\), \(1\le k \le M+1 \), but different values on adjacent intervals. The purpose of segmentation is to determine the value of \(M\), the \(\tau_{k}\) and also the \(\mu_{i}\).
Authors’ abstract: “To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to segment array CGH data are discussed.”
In this paper, the authors consider the following problem. Let \(X_{1},X_{2},\dots,X_{m}\) be independent and normally distributed with variances equal 1. Let us assume that there is \(M\ge 0\) and integers \(0=\tau_{0}<\tau_{1}<\cdots<\tau_{M}<\tau_{M+1}=m\) such that the mean \(\mu_{i}\) of \(X_{i}\), \(1\le i\le m\), is a step function with constant values on each of intervals \(\left(\tau_{k-1},\tau_{k} \right]\), \(1\le k \le M+1 \), but different values on adjacent intervals. The purpose of segmentation is to determine the value of \(M\), the \(\tau_{k}\) and also the \(\mu_{i}\).
Authors’ abstract: “To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic, and give approximations for the probability of a false positive error when there are no change-points. We also study confidence regions based on the likelihood ratio statistic for the change-points and joint confidence regions for the change-points and the parameter values. Applications to segment array CGH data are discussed.”
Reviewer: Wiesław Dziubdziela (Miedziana Góra)
MSC:
| 62G05 | Nonparametric estimation |
| 62G15 | Nonparametric tolerance and confidence regions |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 92D20 | Protein sequences, DNA sequences |
| 62G10 | Nonparametric hypothesis testing |
Keywords:
array CGH analysis; change-points; confidence regions; exponential families; likelihood ratio statistics; comparative genomic hybridization (CGH)Software:
wbsReferences:
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