ترغب بنشر مسار تعليمي؟ اضغط هنا

Studentized U-quantile processes under dependence with applications to change-point analysis

139   0   0.0 ( 0 )
 نشر من قبل Daniel Vogel
 تاريخ النشر 2015
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

Many popular robust estimators are $U$-quantiles, most notably the Hodges-Lehmann location estimator and the $Q_n$ scale estimator. We prove a functional central limit theorem for the sequential $U$-quantile process without any moment assumptions and under weak short-range dependence conditions. We further devise an estimator for the long-run variance and show its consistency, from which the convergence of the studentized version of the sequential $U$-quantile process to a standard Brownian motion follows. This result can be used to construct CUSUM-type change-point tests based on $U$-quantiles, which do not rely on bootstrapping procedures. We demonstrate this approach in detail at the example of the Hodges-Lehmann estimator for robustly detecting changes in the central location. A simulation study confirms the very good robustness and efficiency properties of the test. Two real-life data sets are analyzed.



قيم البحث

اقرأ أيضاً

In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general statistics and lo ng range dependent subordinated Gaussian processes which satisfy mild regularity conditions. We apply our method to a self-normalized change-point test statistic so that we can test for structural breaks in long range dependent time series without having to estimate any nuisance parameter. The finite sample properties are investigated in a simulation study. We analyze three data sets and compare our results to the conclusions of other authors.
80 - Marina Bogomolov 2021
In many statistical problems the hypotheses are naturally divided into groups, and the investigators are interested to perform group-level inference, possibly along with inference on individual hypotheses. We consider the goal of discovering groups c ontaining $u$ or more signals with group-level false discovery rate (FDR) control. This goal can be addressed by multiple testing of partial conjunction hypotheses with a parameter $u,$ which reduce to global null hypotheses for $u=1.$ We consider the case where the partial conjunction $p$-values are combinations of within-group $p$-values, and obtain sufficient conditions on (1) the dependencies among the $p$-values within and across the groups, (2) the combining method for obtaining partial conjunction $p$-values, and (3) the multiple testing procedure, for obtaining FDR control on partial conjunction discoveries. We consider separately the dependencies encountered in the meta-analysis setting, where multiple features are tested in several independent studies, and the $p$-values within each study may be dependent. Based on the results for this setting, we generalize the procedure of Benjamini, Heller, and Yekutieli (2009) for assessing replicability of signals across studies, and extend their theoretical results regarding FDR control with respect to replicability claims.
84 - A. Amiri 2020
We are interested in estimating the location of what we call smooth change-point from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from one level to another which happens smoothly, but over such a small interval, that its length $delta_n$ is considered to be decreasing to $0$ as $nto+infty$. We show that if $delta_n$ goes to zero slower than $1/n$, our model is locally asymptotically normal (with a rather unusual rate $sqrt{delta_n/n}$), and the maximum likelihood and Bayesian estimators are consistent, asymptotically normal and asymptotically efficient. If, on the contrary, $delta_n$ goes to zero faster than $1/n$, our model is non-regular and behaves like a change-point model. More precisely, in this case we show that the Bayesian estimators are consistent, converge at rate $1/n$, have non-Gaussian limit distributions and are asymptotically efficient. All these results are obtained using the likelihood ratio analysis method of Ibragimov and Khasminskii, which equally yields the convergence of polynomial moments of the considered estimators. However, in order to study the maximum likelihood estimator in the case where $delta_n$ goes to zero faster than $1/n$, this method cannot be applied using the usual topologies of convergence in functional spaces. So, this study should go through the use of an alternative topology and will be considered in a future work.
The processes of the averaged regression quantiles and of their modifications provide useful tools in the regression models when the covariates are not fully under our control. As an application we mention the probabilistic risk assessment in the sit uation when the return depends on some exogenous variables. The processes enable to evaluate the expected $alpha$-shortfall ($0leqalphaleq 1$) and other measures of the risk, recently generally accepted in the financial literature, but also help to measure the risk in environment analysis and elsewhere.
Structural changes occur in dynamic networks quite frequently and its detection is an important question in many situations such as fraud detection or cybersecurity. Real-life networks are often incompletely observed due to individual non-response or network size. In the present paper we consider the problem of change-point detection at a temporal sequence of partially observed networks. The goal is to test whether there is a change in the network parameters. Our approach is based on the Matrix CUSUM test statistic and allows growing size of networks. We show that the proposed test is minimax optimal and robust to missing links. We also demonstrate the good behavior of our approach in practice through simulation study and a real-data application.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا