The robustness of the various profile monitoring methods that can perform poorly in the presence of outliers has been heavily debated. To contribute to this strand of the literature, we propose a two-stage outlier detection scheme for non-parametric profile monitoring that can control type-I error rates as well as identify outlier profiles. In the first stage, we define an outlier detection measure by using a non-parametric test statistic and extend the well-known least trimmed squares algorithm to find a clean profile set. Then, in the second stage, the detection of outlying profiles is deemed as a hypothesis testing problem, where the thresholding rule is obtained from the asymptotic distribution of the proposed measure. Furthermore, to enhance efficiency, a one-step refinement algorithm is proposed to determine whether a data point is a real outlying profile. Simulation studies show that the proposed procedure can control type-I error rates, while maintaining reasonably high outlier detection power values. Finally, we apply the proposed approach to a real data analysis to demonstrate the effectiveness of our method. Our approach responds to the fact that in the profile monitoring of statistical process control problems, the dimensionality and complexity of the relationship between the response and explanatory variables can increase the possibility that a profile is outlying and such outlying profiles may influence the data analysis markedly.

In this note, we investigate the existence and asymptotic property of positive periodic solutions to non-autonomous predator-prey system with stage-structured predator on time scales. Via Schauder’s fixed theorem, easily verifiable sufficient existence conditions of positive periodic solutions for the considered system are obtained. We also study asymptotic property of positive periodic solutions on the basis of existence conditions. Due to the symmetry of periodic solutions, the results of this paper have a certain impact on the study of symmetry. It should be pointed out that the system we are studying is built on arbitrary time scale, so our results generalize the results of existing continuous or discrete systems. Furthermore, we develop Schauder’s fixed theorem for studying the delay system on time scales.

This study introduces an innovative two-stage framework for monitoring and diagnosing high-dimensional data streams with sparse changes. The first stage utilizes an exponentially weighted moving average (EWMA) statistic for online monitoring, identifying change points through extreme value theory and multiple hypothesis testing. The second stage involves a fault diagnosis mechanism that accurately pinpoints abnormal components upon detecting anomalies. Through extensive numerical simulations and electron probe X-ray microanalysis applications, the method demonstrates exceptional performance. It rapidly detects anomalies, often within one or two sampling intervals post-change, achieves near 100% detection power, and maintains type-I error rates around the nominal 5%. The fault diagnosis mechanism shows a 99.1% accuracy in identifying components in 200-dimensional anomaly streams, surpassing principal component analysis (PCA)-based methods by 28.0% in precision and controlling the false discovery rate within 3%. Case analyses confirm the method’s effectiveness in monitoring and identifying abnormal data, aligning with previous studies. These findings represent significant progress in managing high-dimensional sparse-change data streams over existing methods.

Model selection is an important tool in statistical inference. However, it is useless with regard to the uncertainty inherent in the inference process. Multicollinearity is a common phenomenon in regression analysis, which can affect the prediction accuracy vastly. This paper introduces a model averaging method called R _p Model Averaging (RMA) to address these two problems simultaneously. Specifically, we use model averaging to deal with uncertainty and ridge estimator to deal with the multicollinearity. Asymptotic optimality of the proposed RMA estimator is derived under some regular conditions. The estimation procedure can be divided into a series of quadratic programming problems and hence easily implemented by existing softwares. Extensive simulation studies show that our proposed method has much better numerical performances in various scenarios. Our method is also employed to a real dataset to illustrate its validity.

A model specification test is a statistical procedure used to assess whether a given statistical model accurately represents the underlying data-generating process. The smoothing-based nonparametric specification test is widely used due to its efficiency against “singular” local alternatives. However, large modern datasets create various computational problems when implementing the nonparametric specification test. The divide-and-conquer algorithm is highly effective for handling large datasets, as it can break down a large dataset into more manageable datasets. By applying divide-and-conquer, the nonparametric specification test can handle the computational problems induced by the massive size of the modern datasets, leading to improved scalability and efficiency and reduced processing time. However, the selection of smoothing parameters for optimal power of the distributed algorithm is an important problem. The rate of the smoothing parameter that ensures rate optimality of the test in the context of testing the specification of a nonlinear parametric regression function is studied in the literature. In this paper, we verified the uniqueness of the rate of the smoothing parameter that ensures the rate optimality of divide-and-conquer-based tests. By employing a penalty method to select the smoothing parameter, we obtain a test with an asymptotic normal null distribution and adaptiveness properties. The performance of this test is further illustrated through numerical simulations.

This article proposes a two-stage process monitoring and fault diagnosis scheme for the high-dimensional data stream. In the first stage, we choose the exponentially weighted moving average (EWMA) statistic to construct the online monitoring statistic, then determine the change point of the data stream based on extreme value theory and multiple hypothesis testing procedures. In the second stage, when the data stream has an abnormal change alarm, it enters an out-of-control state, and we perform a fault diagnosis procedure on the data stream. Specifically, when an abnormal alarm occurs, we further utilize the numerical simulation procedures to detect these components that exhibit anomalies. In addition, to verify the performance of the proposed method, this work also conducts numerical simulations and case studies and compares them with other competitive methods.