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测地线双重差分AI 解读

Summary Difference-in-differences (DID) is a widely used quasi-experimental design for causal inference, traditionally applied to scalar or Euclidean outcomes, while extensions to outcomes residing in non-Euclidean spaces remain limited. Existing methods for such outcomes have primarily focused on univariate distributions, leveraging linear operations in the space of quantile functions, but these approaches cannot be directly extended to outcomes in general metric spaces. In…

重复观测与纵向随机对象的测地线混合效应模型AI 解读

Mixed effect modeling for longitudinal data is challenging when the observed data are random objects, which are complex data taking values in a general metric space without either global linear or local linear (Riemannian) structure. In such settings the classical additive error model and distributional assumptions are unattainable. Due to the rapid advancement of technology, longitudinal data containing complex random objects, such as covariance matrices, data on Riemannian…

时变随机对象与动态网络的建模AI 解读

Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data analysis are infeasible when observations are time courses of networks or other complex non-Euclidean random objects that are elements of general metric spaces. In such spaces, only pairwise distances between the data objects are available and…

以密度为响应的加性函数回归AI 解读

We propose and investigate additive density regression, a novel additive functional regression model for situations where the responses are random distributions that can be viewed as random densities and the predictors are vectors. Data in the form of samples of densities or distributions are increasingly encountered in statistical analysis and there is a need for flexible regression models that accommodate random densities as responses. Such models are of special interest…

条件分位数轨迹的动态建模及其纵向短片段数据应用AI 解读

Longitudinal data are often plagued with sparsity of time points where measurements are available. The functional data analysis perspective has been shown to provide an effective and flexible approach to address this problem for the case where measurements are sparse but their times are randomly distributed over an interval. Here, we focus on a different scenario where available data can be characterized as snippets, which are very short stretches of longitudinal…

重复函数型观测的建模AI 解读

We introduce a new methodological framework for repeatedly observed and thus dependent functional data, aiming at situations where curves are recorded repeatedly for each subject in a sample. Our methodology covers the case where the recordings of the curves are scheduled on a regular and dense grid and also situations more typical for longitudinal studies, where the timing of recordings is often sparse and random. The proposed models lead to an interpretable and…

函数型协变量的条件分位数分析及生长数据应用AI 解读

Summary Motivated by the conditional growth charts problem, we develop a method for conditional quantile analysis when predictors take values in a functional space. The method proposed aims at estimating conditional distribution functions under a generalized functional regression framework. This approach facilitates balancing of model flexibility and the curse of dimensionality for the infinite dimensional functional predictors. Its good performance in comparison with other…

纵向数据的经验动态建模AI 解读

We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth drift process. This equation may be empirically obtained from longitudinal observations for a sample of subjects and does not presuppose specific knowledge of the underlying processes. For the nonparametric estimation of the components of…

纵向数据的函数型变系数模型AI 解读

The proposed functional varying coefficient model provides a versatile and flexible analysis tool for relating longitudinal responses to longitudinal predictors. Specifically, this approach provides a novel representation of varying coefficient functions through suitable auto and cross-covariances of the underlying stochastic processes, which is particularly advantageous for sparse and irregular designs, as often encountered in longitudinal studies. Existing methodology for…

用潜在高斯过程建模稀疏广义纵向观测AI 解读

Summary In longitudinal data analysis one frequently encounters non-Gaussian data that are repeatedly collected for a sample of individuals over time. The repeated observations could be binomial, Poisson or of another discrete type or could be continuous. The timings of the repeated measurements are often sparse and irregular. We introduce a latent Gaussian process model for such data, establishing a connection to functional data analysis. The functional methods proposed are…

函数型与纵向数据分析中主成分方法的性质AI 解读

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of “functional data analysis,” it has often been assumed that a sample of random functions is observed precisely, in the continuum and without noise. While this has been the traditional setting for functional data analysis, in the context of longitudinal data analysis a random function typically represents a patient, or subject, who is observed…

纵向数据的函数型线性回归分析AI 解读

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth random trajectories, and the data consist of a small number of noisy repeated measurements made at irregular times for a sample of subjects. In longitudinal studies, the number of repeated measurements per subject is often small and may…

估计型估计方程：聚类与纵向数据的半参数推断AI 解读

Summary We introduce a flexible marginal modelling approach for statistical inference for clustered and longitudinal data under minimal assumptions. This estimated estimating equations approach is semiparametric and the proposed models are fitted by quasi-likelihood regression, where the unknown marginal means are a function of the fixed effects linear predictor with unknown smooth link, and variance–covariance is an unknown smooth function of the marginal means. We propose…

多元纵向数据的动态相关AI 解读

Nonparametric methodology for longitudinal data analysis is becoming increasingly popular. The analysis of multivariate longitudinal data, where data on several time courses are recorded for each subject, has received considerably less attention, despite its importance for practical data analysis. In particular, there is a need for measures and estimates to capture dependency between the components of vector-valued longitudinal data. We propose and analyze a simple and…

稀疏纵向数据的函数型数据分析AI 解读

We propose a nonparametric method to perform functional principal components analysis for the case of sparse longitudinal data. The method aims at irregularly spaced longitudinal data, where the number of repeated measurements available per subject is small. In contrast, classical functional data analysis requires a large number of regularly spaced measurements per subject. We assume that the repeated measurements are located randomly with a random number of repetitions for…

保序非参数回归及其条件分布与分位数函数估计应用AI 解读

In some regression problems we observe a “response” Yti to level t of a “treatment” applied to an individual with level Xi of a given characteristic, where it has been established that response is monotone increasing in the level of the treatment. A related problem arises when estimating conditional distributions, where the raw data are typically independent and identically distributed pairs (Xi, Zi), and Yti denotes the proportion of Zi's that do not exceed t. We expect the…