Bruce Hoadley
In other FICO Technical Papers, I have shown how to fit Generalized Additive Models (GAM) with shape constraints using quadratic programming applied to B-Spline component functions. In this paper, I extend the method to Robust Least Squares Regression.
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In several FICO studies logistic regression has been shown to be a very competitive technology for developing unrestricted scoring models, especially for performance metrics like ROC area. Application of logistic regression has been hampered by the lack of software to handle complex score engineering such as shape and pattern constraints. The purpose of this paper is to develop a sequential quadratic programming algorithm for score engineered logistic regression. This approach is based on a simple Taylor series expansion of minus log likelihood, which is locally quadratic. and fits in with the…
In this paper we deal with the issue of performing accurate small-sample inference in the Birnbaum-Saunders regression model, which can be useful for modeling lifetime or reliability data. We derive a Bartlett-type correction for the score test and numerically compare the corrected test with the usual score test, the likelihood ratio test and its Bartlett-corrected version. Our simulation results suggest that the corrected test we propose is more reliable than the other tests.
In observational studies, researchers must select a method to control for confounding. Options include propensity score methods and regression. It remains unclear how dataset characteristics (size, overlap in propensity scores, exposure prevalence) influence the relative performance of the methods, making it difficult to select the best method for a particular dataset. A simulation study to evaluate the role of dataset characteristics on the performance of propensity score methods, compared to logistic regression, for estimating a marginal odds ratio in the presence of confounding was conducte…
Understanding Measurement Precision from a Regression Perspective
本文扩展McDonald的回归框架，统一信度与PRMSE为决定系数，提出蒙特卡洛估计方法，并通过因子分析、双参数逻辑及二维IRT树模型验证其适用性。
Smoothed Rank-Based Regression Estimation Using Wilcoxon Score Functions
提出用平滑秩代替整数秩的Wilcoxon秩回归估计，通过核分布函数近似指示函数，在保持稳健性的同时提高重尾误差下的效率并处理结数据，推导了Wald检验并证明渐近正态性。
Inference on multiple quantiles in regression models by a rank-score approach
本文提出一种多变量秩-分数检验的扩展方法，嵌入封闭检验程序以有效处理多重检验问题，并通过理论和模拟研究证明该方法能有效控制家庭错误率并提升统计功效。
PCA score regression: the art of losing power
本文通过理论分析和模拟实验，证明主成分得分回归（RPCS）相比标量函数回归（FoSR）在检测功能数据与协变量关联时存在统计效能损失、α水平膨胀及推断无效的问题，而FoSR通过特定建模工具可避免这些问题。
Debiased Inference on Heterogeneous Quantile Treatment Effects with Regression Rank-Scores
本文提出一种结合 $\ell_1$-惩罚回归调整与秩得分偏差校正的新方法，用于高维协变量下异质性分位数处理效应的去偏推断，并通过模拟和英国生物银行数据验证其有效性。
Background: The development of classification methods for personalized medicine is highly dependent on the identification of predictive genetic markers. In survival analysis it is often necessary to discriminate between influential and non-influential markers. Usually, the first step is to perform a univariate screening step that ranks the markers according to their associations with the outcome. It is common to perform screening using Cox scores, which quantify the associations between survival and each of the markers individually. Since Cox scores do not account for dependencies between the …
Explanations of the internal validity of regression discontinuity designs (RDD) generally appeal to the idea that RDDs are ``as good as" random near the treatment cut point. Cattaneo, Frandsen, and Titiunik (2015) are the first to take this justification to its full conclusion and propose estimating the RDD local average treatment effect (LATE) the same as one would a randomized experiment. This paper explores the implications of analyzing an RDD as a local random experiment when the running variable is a test score. I derive a formula for the bias in the LATE estimate estimated using the loca…
This paper presents a Bayesian approach to multiple-output quantile regression. The unconditional model is proven to be consistent and asymptotically correct frequentist confidence intervals can be obtained. The prior for the unconditional model can be elicited as the ex-ante knowledge of the distance of the tau-Tukey depth contour to the Tukey median, the first prior of its kind. A proposal for conditional regression is also presented. The model is applied to the Tennessee Project Steps to Achieving Resilience (STAR) experiment and it finds a joint increase in tau-quantile subpopulations for …
How to improve the regression factor score predictor when individuals have different factor loadings
针对个体因子载荷存在差异的情形，本文提出基于个体载荷估计和二项检验的异质性回归因子得分预测器，并通过模拟与实证表明其确定性优于传统方法。
This work is motivated by a hand-collected data set from one of the largest Internet portals in Korea. This data set records the top 30 most frequently discussed stocks on its on-line message board. The frequencies are considered to measure the attention paid by investors to individual stocks. The empirical goal of the data analysis is to investigate the effect of this attention on trading behavior. For this purpose, we regress the (next day) returns and the (partially) observed ranks of frequencies. In the regression, the ranks are transformed into scores, for which purpose the identity or li…
In this paper, a practical estimation method for a regression model is proposed using semiparametric efficient score functions applicable to data with various shapes of errors. First, I derive semiparametric efficient score vectors for a homoscedastic regression model without any assumptions of errors. Next, the semiparametric efficient score function can be modified assuming a certain parametric distribution of errors according to the shape of the error distribution or by estimating the error distribution non-parametrically. Nonparametric methods for errors can be used to estimate the paramet…
Propensity score regression for causal inference with treatment heterogeneity
针对异质性处理效应非参数估计计算难、倾向得分极端值下现有方法受限的问题，提出两步非参数的倾向得分回归法，兼具计算优势与理论性质，模拟和真实数据验证了其有效性。
Self and Mauritsen (1988) developed a sample size determination procedure for score tests in generalized linear models under contiguous alternatives. Its performance may deteriorate when the effect size is large. We propose a modification of the Self-Mauritsen method by taking into account of the variance of the score statistic under both the null and alternative hypotheses, and extend the method to noninferiority trials. The modified approach is employed to calculate the sample size for the logistic regression and negative binomial regression in superiority and noninferiority trials. We furth…
We discuss an approach for fitting robust nonlinear regression models, which can be employed to model and predict the contagion dynamics of the Covid-19 in Italy. The focus is on the analysis of epidemic data using robust dose-response curves, but the functionality is applicable to arbitrary nonlinear regression models.
Variable selection is a difficult problem that is particularly challenging in the analysis of high-dimensional genomic data. Here, we introduce the CAR score, a novel and highly effective criterion for variable ranking in linear regression based on Mahalanobis-decorrelation of the explanatory variables. The CAR score provides a canonical ordering that encourages grouping of correlated predictors and down-weights antagonistic variables. It decomposes the proportion of variance explained and it is an intermediate between marginal correlation and the standardized regression coefficient. As a popu…
The permuted score test for robust differential expression analysis
针对负二项回归假设失效导致差异表达分析错误率失控的问题，提出基于置换得分统计量并结合序贯蒙特卡洛与高效GLM算法的检验方法，在保持功效和效率的同时显著改进I类错误控制。
Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which requires only the specification of a distance function. A low-dimensional representation of such distance matrices can be obtained using methods such as multidimensional scaling. Once these variables have been represented as scores, an internal model linking the predictors and the response can be developed using standard methods. We call scoring the transfo…
Outcome Regression Methods for Analyzing Hybrid Control Studies: Balancing Bias and Variability
本文针对混合对照研究，提出增强、G计算和加权回归三种结局回归方法，探讨偏倚与方差权衡，模拟与实例表明加权回归在提升效率方面表现更优。
Propensity score weighted Cox regression for survival outcomes in observational studies with multiple or factorial treatments
本文提出了一种基于倾向评分加权的Cox回归方法，用于估计多重或因子治疗在观察性研究中生存结局的因果危险比，并开发了相应的R包。
Propensity score methods are common for estimating a binary treatment effect when treatment assignment is not randomized. When exposure is measured on an ordinal scale (i.e., low - medium - high), however, propensity score inference requires extensions which have received limited attention. Estimands of possible interest with an ordinal exposure are the average treatment effects between each pair of exposure levels. Using these estimands, it is possible to determine an optimal exposure level. Traditional methods, including dichotomization of the exposure or a series of binary propensity score …
Win-Ratio Regression for Prioritized Composite Outcomes in Observational Studies: Doubly Robust and Efficient Estimation with Future-Score Correction
针对观察性研究中优先复合结局的删失估计问题，提出带未来评分校正的胜比回归框架，结合处理加权与基线增强实现双重稳健高效估计，模拟与OneFlorida数据应用验证了其有效性。
High-dimensional data can be useful for causal inference by providing many confounders that may bolster the plausibility of the ignorability assumption. Propensity score methods are powerful tools for causal inference, are popular in health care research, and are particularly useful for high-dimensional data. Recent interest has surrounded a Bayesian formulation of these methods in order to flexibly estimate propensity scores and summarize posterior quantities while incorporating variance from the (potentially high-dimensional) treatment model. We discuss methods for Bayesian propensity score …
Robust propensity score weighting estimation under missing at random
针对缺失数据下倾向得分加权估计的模型误设问题，本文基于信息投影与内部偏差校准提出一种高效、双重稳健且抗离群值的估计方法，理论性质与模拟均验证了其优越性。
Consider sensitivity analysis for estimating average treatment effects under unmeasured confounding, assumed to satisfy a marginal sensitivity model. At the population level, we provide new representations for the sharp population bounds and doubly robust estimating functions, recently derived by Dorn, Guo, and Kallus. We also derive new, relaxed population bounds, depending on weighted linear outcome quantile regression. At the sample level, we develop new methods and theory for obtaining not only doubly robust point estimators for the relaxed population bounds with respect to misspecificatio…
We propose a novel method for testing the null hypothesis of no effect of a covariate on the response in the context of functional linear concurrent regression. We establish an equivalent random effects formulation of our functional regression model under which our testing problem reduces to testing for zero variance component for random effects. For this purpose, we use a one-sided score test approach, which is an extension of the classical score test. We provide theoretical justification as to why our testing procedure has the right levels (asymptotically) under null using standard assumptio…
On the selection of optimal subdata for big data regression based on leverage scores
本文研究大数据回归中的最优子数据选择问题，将基于杠杆得分的方法从线性模型判别扩展到一阶线性模型和含交互项模型，并通过模拟实验和真实数据应用证明其优于现有方法。
Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to avoid explicit computation of the normalizing constant. In the literature, score matching has so far only been developed for models in which the observations are independent and identically distributed (IID). However, the IID assumption does not hold in the traditional fixed design setting for regression-type models. To deal with the estimation of these covaria…
Ensemble Doubly Robust Bayesian Inference via Regression Synthesis
针对倾向得分与结果模型均可能错误设定的问题，本文提出双重稳健贝叶斯回归合成方法，通过个体自适应集成权重提升因果效应估计的稳健性与不确定性量化能力。
Subsampling is a popular approach to alleviating the computational burden for analyzing massive datasets. Recent efforts have been devoted to various statistical models without explicit regularization. In this paper, we develop an efficient subsampling procedure for the large sample linear ridge regression. In contrast to the ordinary least square estimator, the introduction of the ridge penalty leads to a subtle trade-off between bias and variance. We first investigate the asymptotic properties of the subsampling estimator and then propose to minimize the asymptotic-mean-squared-error criteri…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data is observed for any subject. We consider a regression analysis when the outcome variable and some covariates are collected from two different sources. By leveraging the common variables observed in both data sets, doubly robust estimation procedures are proposed in the literature to protect against possible model misspecifications. However, they employ only …
On regression with estimated covariates and conditional effects given the propensity score
该研究针对协变量需先估计的非参数回归问题，提出两种去偏方法并验证其收敛优势，应用于1997年全国青年纵向调查数据，发现低大学入学概率者完成大学后失业减少更显著。
Statistical Inference for High-Dimensional Robust Linear Regression Models via Recursive Online-Score Estimation
本文提出将递归在线得分估计（ROSE）框架扩展至非凸惩罚M估计，用于稳健高维线性回归的估计与推断，并证明估计量的一致性与渐近正态性，模拟和实际应用验证了其优越性。
The $\infty$-S test via regression quantile affine LASSO
本文提出基于仿射LASSO估计的新型检验方法，利用双变量符号进行评分，用于检验原假设。
Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning
本文指出，在去偏机器学习中，平衡函数应基于奈曼正交分数推导，而非仅作为协变量函数。协变量平衡在回归误差可由协变量表示时有效，但针对处理效应异质性下的ATE估计，分数误差通常包含处理特定成分，因此提倡通过里斯回归实现回归平衡。
Univariate-Guided Sparse Regression for Biobank-Scale High-Dimensional Omics Data
本文提出了一种用于高维组学数据的单变量引导稀疏回归方法，通过两阶段惩罚回归提升特征选择和模型可解释性，并在生物银行数据中实现了预测性能与标准Lasso相当的稀疏模型。
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a slower-than-parametric rate in nonparametric and semiparametric models, and performing calibrated inference can be challenging. In many cases, these estimands can be expressed as the minimizer of a population risk functional. Here, we propose a general framework that leverages such representation and provides a nonparametric extension of the score test for inference on an infini…
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the uncertainty in these selection procedures. In this paper, we propose a new method for inference in high dimensions using a score test based on penalized regression. In this test, we perform penalized regression of an outcome on all but a single feature, and test for correlation of the residuals with the held-out feature. This procedure is applied to each feature in t…
Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over-subscribed schools using randomly assigned lottery numbers, non-lottery tie-breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores and other criteria to rank applicants at ``screened'' schools, combined with lottery tie-breaking at unscreened ``lottery'' schools. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity methods t…
Debiased Inverse Propensity Score Weighting for Estimation of Average Treatment Effects with High-Dimensional Confounders
针对高维混杂下平均处理效应估计问题，提出去偏差逆倾向得分加权法，在倾向得分稀疏逻辑回归假设下获$\bigstar$-相合估计，支持复杂结果回归，可构建置信区间并达半参数效率，已发布R包dipw。
High-dimensional statistical inference for linkage disequilibrium score regression and its cross-ancestry extensions
本文在固定效应数据整合框架下研究连锁不平衡得分回归（LDSC），分析其性能关键因素，揭示其在全基因组变异分析中渐近正态性的可行性与子集分析的挑战，扩展至跨祖先分析并通过真实数据验证。
Conformalized Regression for Continuous Bounded Outcomes
针对连续有界结果的回归问题，提出基于变换回归模型的共形预测区间，使用分位数残差得分处理异方差性和边界不对称性，并证明边际有效性和渐近条件有效性。
In a standard regression problem, we have a set of explanatory variables whose effect on some response vector is modeled. For wide binary data, such as genetic marker data, we often have two limitations. First, we have more parameters than observations. Second, main effects are not the main focus; instead the primary aim is to uncover interactions between the binary variables that effect the response. Methods such as logic regression are able to find combinations of the explanatory variables that capture higher-order relationships in the response. However, the number of explanatory variables t…
Logistic Gaussian process density regression: a generalized Bayesian approach
针对逻辑斯蒂高斯过程密度回归中归一化常数计算困难的问题，提出基于Hyvarinen评分的广义贝叶斯方法，结合稀疏诱导点近似和变分推断实现可扩展性。
Prognostic Covariate Adjustment for Logistic Regression in Randomized Controlled Trials
本文针对二分类终点 RCT 中 Logistic 回归的非可折叠性问题，提出基于生成式 AI 预后评分的协变量调整方法，并结合 g-computation 提升条件与边际因果效应推断的功效和精度。
Covariate Balancing Value Estimation for Optimal Individualized Treatment Rules
提出协变量平衡双重稳健估计量，在倾向得分或规则相关结局回归误差满足特定条件时保证一致性，模拟与白血病数据集应用验证其有效性。
Conformal Calibration for Multi-Modal Regression with Missing Modalities
针对多模态回归中模态缺失或分歧导致预测区间难校准的问题，提出感知模态的共形校准层，在多组实验中提升了区间性能，尤其在模态缺失时恢复了覆盖率。
Effect Identification and Unit Categorization in the Multi-Score Regression Discontinuity Design with Application to LED Manufacturing
本研究提出多评分回归不连续设计中的单元行为分类与模糊性检测方法，通过分解复杂规则改进因果效应估计，并在LED制造数据中验证其降低方差、优化生产政策的有效性。
Tie-breaker experimental designs are hybrids of Randomized Controlled Trials (RCTs) and Regression Discontinuity Designs (RDDs) in which subjects with moderate scores are placed in an RCT while subjects with extreme scores are deterministically assigned to the treatment or control group. In settings where it is unfair or uneconomical to deny the treatment to the more deserving recipients, the tie-breaker design (TBD) trades off the practical advantages of the RDD with the statistical advantages of the RCT. The practical costs of the randomization in TBDs can be hard to quantify in generality, …
Optimal convex $M$-estimation via score matching
本文针对线性回归提出一种基于得分匹配非参数扩展的数据驱动凸损失函数构建方法，该半参数估计量在所有凸 $M$-估计量中达到最小渐近协方差，在保证计算高效与鲁棒性的同时几乎不损失统计效率。
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