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正交与线性回归及共焦二次曲面束AI 解读

This paper enhances and develops bridges between statistics, mechanics, and geometry. For a given system of points in $\mathbb R^k$ representing a sample of full rank, we construct an explicit pencil of confocal quadrics with the following properties: (i) All the hyperplanes for which the hyperplanar moments of inertia for the given system of points are equal, are tangent to the same quadrics from the pencil of quadrics. As an application, we develop regularization…

校准参数的标准误AI 解读

Calibration, the practice of choosing the parameters of a structural model to match certain empirical moments, can be viewed as minimum distance estimation. Existing standard error formulas for such estimators require a consistent estimate of the correlation structure of the empirical moments, which is often unavailable in practice. Instead, the variances of the individual empirical moments are usually readily estimable. Using only these variances, we derive conservative…

含测量误差的函数型数据聚类：一种基于模拟的方法AI 解读

Clustering analysis of functional data, which comprises observations that evolve continuously over time or space, has gained increasing attention across various scientific disciplines. Practical applications often involve functional data that are contaminated with measurement errors arising from imprecise instruments, sampling errors, or other sources. These errors can significantly distort the inherent data structure, resulting in erroneous clustering outcomes. In this…

利用部分网络数据进行干扰效应的模型推断与实验设计AI 解读

The stable unit treatment value assumption states that the outcome of an individual is not affected by the treatment statuses of others, however in many real world applications, treatments can have an effect on many others beyond the immediately treated. Interference can generically be thought of as mediated through some network structure. In many empirically relevant situations however, complete network data (required to adjust for these spillover effects) are too costly or…

合成控制模型中用于供体选择的溢出检测AI 解读

Synthetic control (SC) models are widely used to estimate causal effects in settings with observational time-series data. To identify the causal effect on a target unit, SC requires the existence of correlated units that are not impacted by the intervention. Given one of these potential donor units, how can we decide whether it is in fact a valid donor - that is, one not subject to spillover effects from the intervention? Such a decision typically requires appealing to…

制造业中的因果机器学习决策：是否返工？AI 解读

In this paper, we present a data-driven model for estimating optimal rework policies in manufacturing systems. We consider a single production stage within a multistage, lot-based system that allows for optional rework steps. While the rework decision depends on an intermediate state of the lot and system, the final product inspection, and thus the assessment of the actual yield, is delayed until production is complete. Repair steps are applied uniformly to the lot,…

线上平台的数据驱动实时优惠券分配AI 解读

Traditionally, firms have offered coupons to customer groups at predetermined discount rates. However, advancements in machine learning and the availability of abundant customer data now enable platforms to provide real-time customized coupons to individuals. In this study, we partner with Meituan, a leading shopping platform, to develop a real-time, end-to-end coupon allocation system that is fast and effective in stimulating demand while adhering to marketing budgets when…

HEDE：高维遗传率估计的集成去偏方法AI 解读

Estimating heritability remains a significant challenge in statistical genetics. Diverse approaches have emerged over the years that are broadly categorized as either random effects or fixed effects heritability methods. In this work, we focus on the latter. We propose HEDE, an ensemble approach to estimate heritability or the signal-to-noise ratio in high-dimensional linear models where the sample size and the dimension grow proportionally. Our method ensembles…

不同非比例风险情形下处理效应评价的统计考量AI 解读

We conducted a systematic comparison of statistical methods used for the analysis of time-to-event outcomes under various proportional and nonproportional hazard (NPH) scenarios. Our study used data from recently published oncology trials to compare the Log-rank test, still by far the most widely used option, against some available alternatives, including the MaxCombo test, the Restricted Mean Survival Time Difference (dRMST) test, the Generalized Gamma Model (GGM) and the…

无法直接分配处理时的自适应实验AI 解读

This paper introduces the \emph{confounded pure exploration transductive linear bandit} (\texttt{CPET-LB}) problem. As a motivating example, often online services cannot directly assign users to specific control or treatment experiences either for business or practical reasons. In these settings, naively comparing treatment and control groups that may result from self-selection can lead to biased estimates of underlying treatment effects. Instead, online services can employ…

利用历史实验选择代理指标AI 解读

In many randomized experiments, the treatment effect of the long-term metric (i.e. the primary outcome of interest) is often difficult or infeasible to measure. Such long-term metrics are often slow to react to changes and sufficiently noisy they are challenging to faithfully estimate in short-horizon experiments. A common alternative is to measure several short-term proxy metrics in the hope they closely track the long-term metric -- so they can be used to effectively guide…

无维数结构化协方差估计AI 解读

Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $Σ$ with an additional assumption that $Σ$ can be represented as a sum of a few Kronecker products of smaller matrices. Under mild conditions, we derive the first non-asymptotic dimension-free high-probability bound on the Frobenius distance between $Σ$ and a widely used penalized permuted least squares estimate. Because of the hidden structure,…

Utopia 数据挑战中罕见事件估计的极值方法AI 解读

To capture the extremal behaviour of complex environmental phenomena in practice, flexi\-ble techniques for modelling tail behaviour are required. In this paper, we introduce a variety of such methods, which were used by the Lancopula Utopiversity team to tackle the EVA (2023) Conference Data Challenge. This data challenge was split into four challenges, labelled C1-C4. Challenges C1 and C2 comprise univariate problems, where the goal is to estimate extreme quantiles for a…

粗糙波动率的统计推断：中心极限定理AI 解读

In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter $H < 0.5$. In this paper, we derive a consistent and asymptotically mixed normal estimator of $H$ based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting…

强相关结构下岭插值估计量的精确分析：随机对偶理论视角AI 解读

We consider fully row/column-correlated linear regression models and study several classical estimators (including minimum norm interpolators (GLS), ordinary least squares (LS), and ridge regressors). We show that \emph{Random Duality Theory} (RDT) can be utilized to obtain precise closed form characterizations of all estimators related optimizing quantities of interest, including the \emph{prediction risk} (testing or generalization error). On a qualitative level out…

相关因子回归模型中岭插值器的精确风险分析AI 解读

We consider correlated \emph{factor} regression models (FRM) and analyze the performance of classical ridge interpolators. Utilizing powerful \emph{Random Duality Theory} (RDT) mathematical engine, we obtain \emph{precise} closed form characterizations of the underlying optimization problems and all associated optimizing quantities. In particular, we provide \emph{excess prediction risk} characterizations that clearly show the dependence on all key model parameters,…

存在测量误差时的协变量平衡AI 解读

In recent years, there is a growing body of causal inference literature focusing on covariate balancing methods. These methods eliminate observed confounding by equalizing covariate moments between the treated and control groups. The validity of covariate balancing relies on an implicit assumption that all covariates are accurately measured, which is frequently violated in observational studies. Nevertheless, the impact of measurement error on covariate balancing is unclear,…

法官工具变量设计中的多维聚类AI 解读

Estimates in judge designs run the risk of being biased due to the many judge identities that are implicitly or explicitly used as instrumental variables. The usual method to analyse judge designs, via a leave-out mean instrument, eliminates this many instrument bias only in case the data are clustered in at most one dimension. What is left out in the mean defines this clustering dimension. How most judge designs cluster their standard errors, however, implies that there are…

高效且全局稳健的因果偏离效应估计AI 解读

Causal excursion effect (CEE) characterizes the effect of an intervention under policies that deviate from the experimental policy. It is widely used to study the effect of time-varying interventions that have the potential to be frequently adaptive, such as those delivered through smartphones. We study the semiparametric efficient estimation of CEE and we derive a semiparametric efficiency bound for CEE with identity or log link functions under working assumptions, in the…

改进的经验贝叶斯多元多重检验与效应量估计方法AI 解读

Estimating the sharing of genetic effects across different conditions is important to many statistical analyses of genomic data. The patterns of sharing arising from these data are often highly heterogeneous. To flexibly model these heterogeneous sharing patterns, Urbut et al. (2019) proposed the multivariate adaptive shrinkage (MASH) method to jointly analyze genetic effects across multiple conditions. However, multivariate analyses using MASH (as well as other multivariate…

一般回归误差假设下无岭最小二乘估计量的预测与估计风险AI 解读

In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression error structure, assuming independent and identically distributed errors with zero mean and common variance. In this paper, we explore prediction risk as well as estimation risk under more general regression error assumptions, highlighting…

通过稳健估计处理暴露缺失的因果推断AI 解读

How to deal with missing data in observational studies is a common concern for causal inference. When the covariates are missing at random (MAR), multiple approaches have been provided to help solve the issue. However, if the exposure is MAR, few approaches are available and careful adjustments on both missingness and confounding issues are required to ensure a consistent estimate of the true causal effect on the response. In this article, a new inverse probability weighting…

双向聚类的渐近理论AI 解读

This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an open issue. The existing theory for two-way clustering inference requires identical distributions across clusters (implied by the so-called separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing…

多重线性回归的灵活经验贝叶斯方法及其与惩罚回归的联系AI 解读

We introduce a new empirical Bayes approach for large-scale multiple linear regression. Our approach combines two key ideas: (i) the use of flexible "adaptive shrinkage" priors, which approximate the nonparametric family of scale mixture of normal distributions by a finite mixture of normal distributions; and (ii) the use of variational approximations to efficiently estimate prior hyperparameters and compute approximate posteriors. Combining these two ideas results in fast…