In this study, we focus on high-dimensional time-to-event data in the situation of multiple treatment options. Employing the A-learning framework, we formulate A-learning-based estimating equations and introduce a loss function that can be integrated with regularization penalties. When either the baseline covariate model or the propensity score model is correctly specified, we achieve variable selection for key covariates to optimize treatment decision regimes. Extensive simulation experiments, along with an analysis of the ACTG 175 clinical trial involving HIV-infected patients, validate the effectiveness of the proposed methodology.
Gaussian processes (GP) are known for their outstanding smoothing properties and flexibility in modeling complex nonlinear relationships among variables. Recently, they have been utilized in actuarial science to estimate potential insurance claims. However, in insurance practice, claims data often exhibits non-negative support and asymmetry, resulting in significant model errors when the GP model is employed for claim prediction. This paper intends to replace the Gaussian distribution in GP with a log-Gaussian distribution to construct a log-Gaussian process (LGP) model. The properties and training methods of LGP are discussed. Furthermore, the LGP regression model is employed for estimating claims reserve. It is shown that the LGP regression model offers higher prediction accuracy and reliability compared to other models, particularly the GP regression model, making it more suitable for claims reserving.
Conditional Value-at-Risk (CVaR) is a widely used coherent risk measure in the finance and machine learning communities to ensure robustness and fairness. Focusing on CVaR portfolio optimization problems in the expanding global markets, this paper analyzes sparsity-induced portfolio strategies. We first analyze the equivalence of the regularized CVaR minimization problem and its l(0)-constrained counterpart in the norm ball, which suggests the validity of regularizers for sparsity-induced CVaR minimization. Furthermore, we establish the finite-sample statistical estimation error rate for the proposed method in the ultrahigh-dimensional scenario, when the number of assets under management can scale exponentially with the sample size of the historical data. The numerical experiments demonstrate the risk aversion preference and robustness of the proposed portfolio strategy on both synthetic data and the S&P 500 dataset. the to forced mittee foundations, mization hedging ippi of a markets quately they the ceed the U.S.
In longitudinal follow-up studies, recurrent event data with a terminal event are frequently encountered. In certain situations, some subjects drop out of the study for a period of time for various reasons before returning to the study again and this may happen more than once. Disregarding these gaps and treating the data as a regular recurrent event dataset may lead to biased estimations and potentially misleading conclusions. In this paper, we propose a flexible additive-multiplicative rates model for the analysis of recurrent event data with a terminal event and multiple intermittent gaps. This model allows for both additive and multiplicative effects of covariates, while leaving the dependence structure among the recurrent and terminal events unspecified. To infer the parameters of interest in the proposed model, we construct unbiased estimating equations and establish the asymptotic properties of the resulting estimators. Simulation studies demonstrate that considering intermittent gaps yields more accurate estimations in finite samples compared to the naive method. An application to a medical cost study of chronic heart failure is provided for illustration.
Panel data offers valuable insights into both temporal and cross-sectional variations, making it essential for analyzing complex problems. To address dimensionality reduction challenges in high-dimensional varying coefficient panel data models with fixed effects, we propose a novel variable selection method that combines basis function approximation with non-convex group penalties (SCAD/MCP). Using auxiliary regression and orthogonal projection, we isolate fixed effects to prevent their interference in variable selection. Basis function expansion approximates nonlinear coefficients, enabling simultaneous identification of the true model structure and estimation of non-zero coefficients. Under some regularity conditions, our method consistently identifies the true model, with the estimator exhibiting the oracle property. We employ a group descent algorithm to solve the penalized objective function. Simulation studies demonstrate that SCAD and MCP outperform Lasso in variable selection accuracy, reducing false positives and enhancing coefficient estimation. When applied to real data, our method effectively identifies important variables and delivers superior predictive performance.
