In the medical status forecasting context, the autocorrelation and categorical variable properties of the changing status bring difficulties in the data modeling. The parameter value and model performance demonstrate varying among different individuals with different demographic baseline information. To overcome these difficulties, a new modeling strategy is established to forecast the Markov transition state with the response variable modified as the transition type instead of the original state. In the subgroup analysis, model ANOVA and CTree are proposed to explore the influence of baseline information on the parameters and model performance. The results show that the developed model achieves prominently satisfying performance with wholly higher AUC value for both the simulated data and real data. For the method SVM, the AUC value obviously increases from 0.646 to 0.803. The subgroup analysis considers the individual-specific effect existing in different individuals. From the simulation, the mean value of AUC increases by around 0.1 using SVM, RF and NNET and the median value increases by 0.2 through the real data analysis using SVM with Markov transformed response variable, which validate the effectiveness of the proposed scheme of status forecasting.
Autoregressive (AR) models play an important role in time series analysis. For AR models with missing data, existing methods fully exploit the temporal structure to impute missing values. This paper extends these imputation approaches to quantile regression (QR), leveraging information from observations before and after missing values. Within a Bayesian framework, LASSO-type priors are imposed on both the regression coefficients and the autoregressive parameters. A Gibbs-sampling-based imputation method is proposed to simultaneously generate posterior samples for parameter estimation and variable selection. To assess the sensitivity of the partially functional linear model with autoregressive errors and missing data to minor perturbations or influential observations, a Bayesian local influence analysis is conducted. This fills a gap in statistical diagnostics for QR models with autoregressive errors and missing data. Simulation studies evaluate the performance of the proposed method under varying missing rates. The approach is applied to real electricity consumption data to demonstrate its validity and feasibility.
This paper proposes a unified Bayesian framework for detecting structural changes in dependent binary time series while simultaneously selecting active covariates within each regime. Addressing the limitations of independence assumptions in standard methods, we explicitly model serial dependence through a conditional dynamic logit specification. We employ a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm coupled with a Stochastic Search Variable Selection (SSVS) prior to handle dimension variation and enforce sparsity in multivariate and moderate-dimensional settings. To ensure computational efficiency, we integrate the Pólya–Gamma data augmentation scheme, which facilitates the analytical integration of the logistic likelihood and enables exact block-updates for regression coefficients. Simulation studies demonstrate the method’s robustness in correctly identifying the number of time intervals and relevant predictors under multicollinearity. Application to S P 500 market data reveals distinct directional regimes during the financial crisis, validating the model’s practical utility for real-world inference.
Variable selection in logistic regression with correlated predictors is a challenging problem. Ridge-type estimators stabilize estimation under multicollinearity but yield dense models, whereas sparsity-inducing penalties such as LASSO and elastic net may overselect noise variables and do not explicitly preserve the ridge stabilization mechanism. We propose a Ridge Selection Operator (RSO) for logistic regression by extending individually penalized ridge regression within an iteratively reweighted least squares (IRLS) framework. Predictor-specific penalty weights are estimated under a simplex constraint, allowing automatic allocation of regularization across predictors. Sparsity is induced by concentrating the penalty weight on selected components, effectively shrinking irrelevant coefficients to zero. Adaptive and modified variants of RSO are developed to further enhance variable selection performance. The proposed ℓ _2 + simplex constraint formulation is shown to offer distinct advantages over both ridge regression and ℓ _1 -based methods, particularly under moderate to strong predictor correlation ( ρ≥ 0.6 ), where ℓ _1 -based methods are most prone to arbitrary selection and inflated false discovery rates. A comprehensive Monte Carlo simulation study evaluates performance across 168 configurations spanning varying sample sizes, dimensionality levels, correlation structures, and signal strengths including weak and moderate signal scenarios designed to provide a more challenging evaluation. Selection frequencies, true positive rates (TPR), true negative rates (TNR), sparsity recovery, and binomial deviance are assessed across competing methods. Variable inclusion heatmaps and coefficient regularization paths illustrate the selection behavior and shrinkage dynamics of the proposed estimators. The results demonstrate that adaptive RSO-type methods achieves improved noise exclusion and more reliable sparsity recovery compared to LASSO and elastic net, while maintaining stable estimation under strong correlation.
The L^p -quantile regression framework, defined through an L^p -type asymmetric loss with 1
