论文检索

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…

通过变系数模型进行协变量调整回归推断AI 解读

We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable covariate, where one specific distorting function is associated with each predictor or response. The dependence of both response and predictors on the same confounding covariate may alter the underlying regression relation between…

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…

广义函数型线性模型AI 解读

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function, and the expected value of the response is related to this linear predictor via a link function. If, in addition, a variance function is specified, this leads to a functional estimating…

协变量调整回归AI 解读

We introduce covariate-adjusted regression for situations where both predictors and response in a regression model are not directly observable, but are contaminated with a multiplicative factor that is determined by the value of an unknown function of an observable covariate. We demonstrate how the regression coefficients can be estimated by establishing a connection to varying-coefficient regression. The proposed covariate-adjustment method is illustrated with an analysis…

时间扭曲随机曲线的函数凸平均与同步AI 解读

Data that can be best described as a sample of curves are now fairly common in science and engineering. When the dynamics of development, growth, or response over time are at issue, subjects or experimental units may experience events at different temporal paces. For functional data where trajectories may be individually time-transformed, it is usually inadequate to use commonly used sample statistics, such as the cross-sectional mean or median or the cross-sectional sample…

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…

具有平滑随机效应的函数型准似然回归模型AI 解读

Summary We propose a class of semiparametric functional regression models to describe the influence of vector-valued covariates on a sample of response curves. Each observed curve is viewed as the realization of a random process, composed of an overall mean function and random components. The finite dimensional covariates influence the random components of the eigenfunction expansion through single-index models that include unknown smooth link and variance functions. The…

不连续回归与平滑回归的比较AI 解读

Z.Given measurements $(x_i,y_i) = 1,\dots,n$, we discuss methods to assess whether an underlying regression function is smooth (continuous or differentiable) or whether it has discontinuities. The variance of the measurements is assumed to be unknown, and is estimated simultane-ously. By regressing squared differences of the data formed with various span sizes on the span size itself, we obtain an asymptotic linear model with dependent errors. The parameters of this…

The quasi-likelihood function proposed by Wedderburn broadened the scope of generalized linear models by specifying the variance function in-stead of the entire distribution. However, complete specification of variance functions in the quasi-likelihood approach may not be realistic. We define a nonparametric quasi-likelihood by replacing the specified variance function in the conventional quasi-likelihood with a nonparametric variance function estimate. This nonparametric…

连接函数与方差函数未知时的拟似然回归AI 解读

We consider the multiple regression model E(y) = μ, μ = g(x T β), var(y) — [sgrave]2(μ) with predictors x, link function g, and variance function [sgrave]2(·). The aim is to reduce the assumptions in a fully parametric generalized linear model or a quasi-likelihood model by allowing the link and the variance functions to be unknown but smooth. These functions are then estimated nonparametrically, and the estimates are substituted into the quasi-likelihood function. We…

最高龄死亡率分析：重新审视生命表AI 解读

This paper provides a data analysis and some methodological advances which contribute to an ongoing scientific debate about the patterns of aging. One of the problems we address is how to estimate a hazard function when only aggregated information on the lifetimes in the form of a lifetable is available. This problem affects the the estimation of oldest-old mortality which in turn plays an important role in the quantification of biological lifespan and longevity. We…

重复测量剂量—反应关系的随机效应阈值模型AI 解读

Summary A random threshold model for dose--response designs with repeated measurements is introduced. Inference procedures for this model are discussed. The framework of generalized linear models is used to propose a quasi-likelihood inference procedure. The feasibility of this approach is illustrated with the analysis of food science data concerning a forced choice sensory experiment.

响应曲线的时间加速模型AI 解读

We propose a nonparametric method of data analysis for situations where the data consist of a sample of curves and a covariate is present. We assume the observed curves to be time-accelerated versions of a basic underlying stochastic process and assume the time acceleration factor for each observed process, determining the “eigenzeit,” to be a smooth function of the covariate. We discuss an iterative procedure to estimate the components of the model nonparametrically, using…

地理聚合数据的空间平滑及发病率地图构建AI 解读

We address the commonly encountered situation in spatial statistics where data such as counts of incidences of a certain disease are available only in geographically aggregated form. We develop fairly general models and propose a modified version of the locally weighted least squares method to recover the unknown smooth spatial function that is assumed to generate the observations. In the special case of count data, the target function is the intensity function, conditional…

用于曲面平滑与偏导数估计的预平均局部正交多项式估计量AI 解读

We propose a multivariate smoothing method based on products of localized orthogonal polynomial series estimators for a smooth regression surface in the fixed-design regression model. The estimation of partial derivatives is included. The proposed method provides for automatic and efficient boundary modifications near the edges of the surface, assuming that the boundary of the support of the regression function satisfies some regularity conditions. By allowing for a…

端点附近的平滑最优核估计量AI 解读

Kernel estimators for smooth curves like density, spectral density or regression functions require modifications when estimating near endpoints of the support, both for practical and asymptotic reasons. The construction of such boundary kernels as solutions of a variational problem is addressed and representations in orthogonal polynomials are given, including explicit solutions for the most important cases. Based on explicit formulae for certain functional of the kernels,…

删失生存数据中风险率变化的非参数分析：变点模型的替代方案AI 解读

As a nonparametric estimator for the point of the most rapid change of a hazard rate we propose the location of an extremum of a nonparametric estimate of the derivative, or equivalently, of a zero of a nonparametric estimate of the second derivative. Using the kernel method for the nonparametric estimation of derivatives of the hazard rate, the asymptotic local limiting distribution and uniform consistency are applied to prove consistency and to find the limiting…

二元反应生物测定中的核估计与 Probit 估计AI 解读

A kernel method for the estimation of quantal dose-response curves is considered. In contrast to parametric modeling, this local smoothing method does not require any assumptions beyond smoothness of the dose-response curve and, in this sense, is nonparametric. In finite-sample situations, the kernel estimate of the dose-response curve is not necessarily monotone and, therefore, if the additional assumption of monotonicity of the dose-response curve is made, a monotonized…

非参数曲线拟合中的加权局部回归与核方法AI 解读

Weighted local regression, a popular technique for smoothing scatterplots, is shown to be asymptotically equivalent to certain kernel smoothers. Since both methods are local weighted averages of the data, it is proved that in the fixed design regression model, given a weighted local regression procedure with any weight function, there is a corresponding kernel method such that the quotients of weights distributed by both methods tend uniformly to 1 as the number of…

含噪数据导数估计的带宽选择与置信区间AI 解读

We propose a method for automatic bandwidth selection for kernel estimators of derivatives of a regression function. The finite sample behaviour of this new method is compared with that of other methods in a Monte Carlo Study. The automatic estimation of derivatives can be employed for the construction of asymptotic local confidence intervals for the nonparametric estimate of the regression function and its first derivatives.