This work proposes a two-stage procedure for identifying outlying observations in a large-dimensional data set. In the first stage, an outlier identification measure is defined by using a max-normal statistic and a clean subset that contains non-outliers is obtained. The identification of outliers can be deemed as a multiple hypothesis testing problem, then, in the second stage, we explore the asymptotic distribution of the proposed measure, and obtain the threshold of the outlying observations. Furthermore, in order to improve the identification power and better control the misjudgment rate, a one-step refined algorithm is proposed. Simulation results and two real data analysis examples show that, compared with other methods, the proposed procedure has great advantages in identifying outliers in various data situations.

The independence assumption would lead to poor estimation of the availability and even misleading conclusions when dependence actually exists. In this paper, we provide the estimation of the limiting availability of a repairable series system when the failure times and repair times are two independent sequences of stationary dependent random variables. Furthermore, consistency and asymptotic normality of the estimator of the limiting availability are derived under some regular conditions. Finally, we investigate the limiting availability for a first-order exponential moving average (EMA1) process and a first-order exponential autoregressive (EAR(1)) process. Simulations are presented to study the impact of dependence on the estimation of the limiting availability.

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.

In this paper, we investigate robust model averaging for high-dimensional data with outlier contamination. Most existing model averaging methods rely on ordinary least squares (OLS) estimation and are therefore highly sensitive to outliers. Moreover, these methods are generally not designed to accommodate high-dimensional settings. To overcome these limitations, we propose a robust fast greedy model averaging (Robust FGMA) method. The proposed approach incorporates the Huber robust loss function and fold-specific median absolute deviation (MAD) scale estimation into the cross-validation weight-selection criterion within the fast greedy model averaging (FGMA) framework. Simulation studies demonstrate that Robust FGMA achieves superior predictive accuracy and stability under various contamination and high-dimensional scenarios. Furthermore, empirical analysis based on the real biological dataset GSE10245 supports the effectiveness of the proposed method in the presence of outliers. The proposed approach retains the accelerated weight optimization structure of FGMA and is applicable to high-dimensional regression settings.