Regression Analysis by Example.
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实例回归分析AI 解读 ↓
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Simple Linear Regression Multiple Linear Regression Regression Diagnostics: Detection of Model Violations Qualitative Variables as Predictors Transformation of Variables Weighted Least Squares The Problem of Correlated Errors Analysis of Collinear Data Biased Estimation of Regression Coefficients Variable Selection Procedures Logistic Regression Appendix References Index.
Understanding associations between paired high-dimensional longitudinal datasets is a fundamental yet challenging problem arising across scientific domains, including longitudinal multi-omic studies. The difficulty stems from the complex, time-varying cross-covariance structure coupled with high dimensionality, which complicates both model formulation and statistical estimation for association discovery. To address these challenges, we propose a new framework called…
结合 model-X knockoffs 与 p 值的高维线性模型 FDR 控制
We propose a novel multiple testing methodology for controlling the false discovery rate (FDR) in high-dimensional linear models that integrates model-X knockoff techniques with debiased penalized regression estimators. At the foundation of our methodology, we construct and study two sets of naturally paired high-dimensional test statistics and the associated $p$-values for evaluating the same null hypotheses. The first set is shown to be asymptotically mutually independent,…
基于广义逆距离权重的GNAR模型改进多元时间序列预测
Many multivariate time series arise on networks where relationships between variables depend on physical or more general distances. Standard vector autoregressive models struggle in such settings due to their quadratic parameter growth, while generalised network autoregressive (GNAR) models offer a parsimonious alternative by explicitly incorporating network structures. Existing GNAR formulations assume fixed weights, typically uniform or reciprocal distances, which may not…
We consider the joint estimation of change-point locations and the sparsity pattern of the variance-covariance matrix, which is assumed to evolve in a piecewise constant manner. By applying Group Fused LASSO and LASSO penalties to the squared Frobenius norm, we estimate both the covariance structure and the change points. Adaptive weights are incorporated into the penalty terms to enhance change-point detection and covariance estimation accuracy. We establish the conditions…
近端估计与推断
Abstract We develop a convex-analytic framework for constructing and analyzing a broad class of penalized estimators. Our method defines penalized estimators by applying proximal operators to benchmark estimators, rather than by penalizing the benchmark criterion itself. We establish general finite-sample properties, derive unified asymptotic distribution results, and provide tractable conditions for oracle selection and oracle asymptotic efficiency. We then apply the…
组间不平衡下的风险异质性稳健推断
Population-level heterogeneity is ubiquitous in biomedical data, where differences across demographic or clinical subgroups can substantially alter risk patterns. For example, in intensive care unit (ICU) studies, the mortality risk associated with specific admission diagnoses can vary across ethnic groups. Existing approaches for detecting risk heterogeneity are often sensitive to baseline model misspecification and regularization bias, both of which commonly arise in…