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We study the maximum score statistic to detect and estimate local signals in the form of change-points in the level, slope, or other property of a sequence of observations, and to segment the sequence when there appear to be multiple changes. We find that when observations are serially dependent, the change-points can lead to upwardly biased estimates of autocorrelations, resulting in a sometimes serious loss of power. Examples involving temperature variations, the level of atmospheric greenhouse gases, suicide rates and daily incidence of COVID-19 illustrate the general theory.
A novel sequential change detection problem is proposed, in which the change should be not only detected but also accelerated. Specifically, it is assumed that the sequentially collected observations are responses to treatments selected in real time.
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently estimate,
Additive models, as a natural generalization of linear regression, have played an important role in studying nonlinear relationships. Despite of a rich literature and many recent advances on the topic, the statistical inference problem in additive mo
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and when we on
We study nonparametric maximum likelihood estimation of a log-concave probability density and its distribution and hazard function. Some general properties of these estimators are derived from two characterizations. It is shown that the rate of conve