This paper investigates sequential change-point detection in reconfigurable sensor networks. In this problem, data from multiple sensors are observed sequentially. Each sensor can have a unique change point, and the data distribution differs before and after the change. We aim to detect these changes as quickly as possible once they have occurred while controlling the false discovery rate at all times. Our setting is more realistic than traditional settings in that (1) the set of active sensors – i.e., those from which data can be collected – can change over time through the deactivation of existing sensors and the addition of new sensors, and (2) dependencies can occur both between sensors and across time points. We propose powerful e-value-based detection procedures that control the false discovery rate uniformly over time. Numerical experiments demonstrate that, with the same false discovery rate target, our procedures achieve superior performance compared to existing methods, exhibiting lower false non-discovery rates and reduced detection delays.

This note studies matrix completion for a partially observed $n$ by $p$ data matrix involving mixed types of variables (e.g., continuous, binary, ordinal). A general family of non-linear factor models is considered, under which the matrix completion problem becomes the estimation of an $n$ by $p$ low-rank matrix ${\mathbf M}$. For existing methods in the literature, estimation consistency is established by showing $\Vert \hat {\mathbf M} - {\mathbf M}^*\Vert_F/\sqrt{np}$, the scaled Frobenius norm of the difference between the estimated and true ${\mathbf M}$ matrices, converges to zero in probability as $n$ and $p$ grow to infinity. However, this notion of consistency does not guarantee the convergence of each individual entry and, thus, may not be sufficient when specific data entries or the worst-case scenario is of interest. To address this issue, we consider the notion of entrywise consistency based on $\Vert \hat {\mathbf M} - {\mathbf M}^* \Vert_{\mbox{max}}$, the max norm of the estimation error matrix. We propose refinement procedures that turn estimators, which are consistent in the Frobenius norm sense, into entrywise estimators through a one-step refinement. Tight probabilistic error bounds are derived for the proposed estimators. The proposed methods are evaluated by simulation studies and real-data applications for collaborative filtering and large-scale educational assessment.

We consider the statistical inference for noisy incomplete binary (or 1-bit) matrix. Despite the importance of uncertainty quantification to matrix completion, most of the categorical matrix completion literature focuses on point estimation and prediction. This paper moves one step further toward statistical inference for binary matrix completion. Under a popular nonlinear factor analysis model, we obtain a point estimator and derive its asymptotic normality. Moreover, our analysis adopts a flexible missing-entry design that does not require a random sampling scheme as required by most of the existing asymptotic results for matrix completion. Under reasonable conditions, the proposed estimator is statistically efficient and optimal in the sense that the Cramer-Rao lower bound is achieved asymptotically for the model parameters. Two applications are considered, including (1) linking two forms of an educational test and (2) linking the roll call voting records from multiple years in the United States Senate. The first application enables the comparison between examinees who took different test forms, and the second application allows us to compare the liberal-conservativeness of senators who did not serve in the Senate at the same time.

Multidimensional unfolding methods are widely used for visualizing item response data. Such methods project respondents and items simultaneously onto a low-dimensional Euclidian space, in which respondents and items are represented by ideal points, with person-person, item-item, and person-item similarities being captured by the Euclidian distances between the points. In this paper, we study the visualization of multidimensional unfolding from a statistical perspective. We cast multidimensional unfolding into an estimation problem, where the respondent and item ideal points are treated as parameters to be estimated. An estimator is then proposed for the simultaneous estimation of these parameters. Asymptotic theory is provided for the recovery of the ideal points, shedding lights on the validity of model-based visualization. An alternating projected gradient descent algorithm is proposed for the parameter estimation. We provide two illustrative examples, one on users' movie rating and the other on senate roll call voting.