This study introduces a sign-constrained L_1 -penalized logistic regression to analyze aggregated binary data, inspired by privacy-preserving epidemiological investigations during the COVID-19 pandemic. We consider two types of binary data aggregation: the total number of events occurring in each region and the presence or absence of at least one event in each region. To accommodate these two types of aggregated binary data, we first formulate the likelihood functions for privacy-preserving logistic regression and establish the asymptotic behaviors of the resulting maximum likelihood estimators. We then propose the sign-constrained L_1 -penalized logistic regression and develop an efficient computational algorithm for estimating the regression coefficients. In particular, the proposed method integrates sign constraints on the regression coefficients to enhance interpretability, thereby improving communication between policymakers and biostatisticians. We demonstrate the effectiveness of the proposed method through numerical studies and real data analysis.
In the era of big data, matrix data appear frequently in modern scientific applications, such as electroencephalography (EEG) data, excitation-emission matrix (EEM) data, and colorimetric sensor array data. Some application data, such as stocks data, may not appear to be in matrix form, but we can reformulate it into matrix data. To the end of finding the group structure in these datasets, we propose a matrix sparse group Lasso variable selection and estimation method for data with high-dimensional predictors. The method is carried out through a penalized matrix regression model with an arbitrary group structure for the regression coefficient matrix. For the new proposed model, we establish the oracle bounds for the prediction error, the estimation error, and the order of sparsity. In order to get the estimator of the new model, we design a mixed coordinate descent algorithm. The numerical studies show that our model can select the group structure and sparsity accurately and effectively. Especially, we used the new model to predict the movements of some stocks selected from NASDAQ Stock Market.
The paper deals with models in which the dependent variable, some explanatory variables, or both represent unobserved sensitive data. We introduce a novel discretization method that reveals sufficient information from the sensitive variable to approximate the parameter(s) of interest. Multiple discretization schemes are employed, and we show convergence in distribution for the unobserved variable. The asymptotic properties of the OLS estimator for linear models are derived and discussed. Monte Carlo simulations support our theoretical findings and demonstrate finite-sample properties. Finally, we contrast our method with other alternative methods for estimating the Australian gender wage gap.
Categorical variables collected through surveys often share a high degree of information, leading to substantial redundancy. If not properly accounted for, redundant information may result in misleading outcomes when distance-based techniques are applied, such as data visualization and profiling via Multidimensional Scaling (MDS). This issue typically arises when additive dissimilarity coefficients are employed in datasets characterized by moderate to strong associations among variables. In this work, we propose new dissimilarities for categorical data that explicitly account for the association structure of the data. These dissimilarities are subsequently combined with a robust distance for numerical variables, yielding a flexible and robust metric for multivariate heterogeneous data. The performance of the proposed metrics is evaluated under adverse scenarios involving underlying correlation structures and outlier contamination, and is compared with that of the classical Gower distance using MDS representations and a Nearest Neighbor classifier. In addition, the proposed methodology is illustrated through three real-data applications, addressing both profiling and classification tasks. The results show that the proposed distances are effective in isolating outlying units and in improving classification accuracy.
Missing values in multivariate dependent variables may occur during data collection, requiring imputation methods capable of handling complex inter-variable relationships. We propose a nonparametric copula-based method for imputing dependent multivariate missing data, called NPCoImp. By leveraging the empirical beta copula to calculate the conditional cumulative probability function of the missing variables given the observed ones, NPCoImp imputes data while respecting the underlying distributional shape - particularly radial symmetry - and accordingly adjusts the multivariate values used for imputation. NPCoImp is highly flexible and can handle multivariate missing data with any type of missingness pattern. The performance of NPCoImp has been evaluated through an extensive Monte Carlo study and compared with classical imputation methods, as well as with its direct competitor, the CoImp algorithm, and a machine learning-based technique, the missForest. Our findings indicate that NPCoImp is particularly effective in preserving complex dependence structure irrespective of the sample size, the proportion of missing data and the strength of the dependence. The strong performance of the proposed method is further supported by empirical case studies in the agricultural sector. Finally, the NPCoImp algorithm has been implemented in the R package CoImp, which is available on CRAN.
