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测量误差下删失分位数回归的平滑与校正得分方法AI 解读

Censored quantile regression is an important alternative to the Cox proportional hazards model in survival analysis. In contrast to the usual central covariate effects, quantile regression can effectively characterize the covariate effects at different quantiles of the survival time. When covariates are measured with errors, it is known that naively treating mismeasured covariates as error-free would result in estimation bias. Under censored quantile regression, we propose…

重复测量结果的函数单指标广义部分线性模型：核与样条融合平滑AI 解读

We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single…

用验证信息准则确定降维模型的结构维数AI 解读

A crucial component of performing sufficient dimension reduction is to determine the structural dimension of the reduction model. We propose a novel information criterion-based method for this purpose, a special feature of which is that when examining the goodness-of-fit of the current model, one needs to perform model evaluation by using an enlarged candidate model. Although the procedure does not require estimation under the enlarged model of dimension k+1, the decision as…

协变量同时含测量误差与误分类时的函数型和结构型方法AI 解读

Covariate measurement imprecision or errors arise frequently in many areas. It is well known that ignoring such errors can substantially degrade the quality of inference or even yield erroneous results. Although in practice both covariates subject to measurement error and covariates subject to misclassification can occur, research attention in the literature has mainly focused on addressing either one of these problems separately. To fill this gap, we develop estimation and…

中心均值子空间的估计效率AI 解读

Summary We investigate the estimation efficiency of the central mean subspace in the framework of sufficient dimension reduction. We derive the semiparametric efficient score and study its practical applicability. Despite the difficulty caused by the potential high dimension issue in the variance component, we show that locally efficient estimators can be constructed in practice. We conduct simulation studies and a real data analysis to demonstrate the finite sample…

微分方程参数的快速简便一步估计AI 解读

Summary Differential equations are customarily used to describe dynamic systems. Existing methods for estimating unknown parameters in those systems include parameter cascade, which is a spline-based technique, and pseudo-least-squares, which is a local-polynomial-based two-step method. Parameter cascade is often referred to as a ‘one-step method’, although it in fact involves at least two stages: one to choose the tuning parameter and another to select model parameters. We…

任意样本选择偏差下未知对称总体的半参数有效稳健估计AI 解读

We propose semiparametric methods to estimate the center and shape of a symmetric population when a representative sample of the population is unavailable due to selection bias. We allow an arbitrary sample selection mechanism determined by the data collection procedure, and we do not impose any parametric form on the population distribution. Under this general framework, we construct a family of consistent estimators of the center that is robust to population model…

允许高维协变量的异方差部分线性单指标模型：双重稳健与有效估计AI 解读

Summary We study the heteroscedastic partially linear single-index model with an unspecified error variance function, which allows for high dimensional covariates in both the linear and the single-index components of the mean function. We propose a class of consistent estimators of the parameters by using a proper weighting strategy. An interesting finding is that the linearity condition which is widely assumed in the dimension reduction literature is not necessary for…

充分降维中的有效估计AI 解读

We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the optimal semiparametric efficiency bound. The resulting efficient estimator can exhaustively estimate the central subspace…

删失混合数据的非参数估计及亨廷顿病观察研究应用AI 解读

This work presents methods for estimating genotype-specific distributions from genetic epidemiology studies where the event times are subject to right censoring, the genotypes are not directly observed, and the data arise from a mixture of scientifically meaningful subpopulations. Examples of such studies include kin-cohort studies and quantitative trait locus (QTL) studies. Current methods for analyzing censored mixture data include two types of nonparametric maximum…

响应缺失与协变量测量误差下纵向研究的函数型广义矩方法AI 解读

Abstract Covariate measurement error and missing responses are typical features in longitudinal data analysis. There has been extensive research on either covariate measurement error or missing responses, but relatively little work has been done to address both simultaneously. In this paper, we propose a simple method for the marginal analysis of longitudinal data with time-varying covariates, some of which are measured with error, while the response is subject to…

降维问题的半参数方法AI 解读

We provide a novel and completely different approach to dimension-reduction problems from the existing literature. We cast the dimension-reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension reduction techniques as special cases in this class. The semiparametric approach also reveals that in the inverse regression…

总体归属不确定时多个总体的密度估计AI 解读

We devise methods to estimate probability density functions of several populations using observations with uncertain population membership, meaning from which population an observation comes is unknown. The probability of an observation being sampled from any given population can be calculated. We develop general estimation procedures and bandwidth selection methods for our setting. We establish large-sample properties and study finite-sample performance using simulation…

测量误差模型中的鞍点检验AI 解读

We develop second-order hypothesis testing procedures in functional measurement error models for small or moderate sample sizes, where the classical first-order asymptotic analysis often fails to provide accurate results. In functional models no distributional assumptions are made on the unobservable covariates and this leads to semiparametric models. Our testing procedure is derived using saddlepoint techniques and is based on an empirical distribution estimation subject to…

经典测量误差模型中的局部与总体拟合优度检验AI 解读

Summary We consider functional measurement error models, i.e. models where covariates are measured with error and yet no distributional assumptions are made about the mismeasured variable. We propose and study a score-type local test and an orthogonal series-based, omnibus goodness-of-fit test in this context, where no likelihood function is available or calculated—i.e. all the tests are proposed in the semiparametric model framework. We demonstrate that our tests have…

半参数广义线性潜变量模型的显式估计方程AI 解读

Summary We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit…

微阵列数据分析中的方差估计AI 解读

Summary Microarrays are one of the most widely used high throughput technologies. One of the main problems in the area is that conventional estimates of the variances that are required in the t-statistic and other statistics are unreliable owing to the small number of replications. Various methods have been proposed in the literature to overcome this lack of degrees of freedom problem. In this context, it is commonly observed that the variance increases proportionally with…

协变量变换下含测量误差的治愈率模型AI 解读

Cure rate models explicitly account for the survival fraction in failure time data. When the covariates are measured with errors, naively treating mismeasured covariates as error-free would cause estimation bias and thus lead to incorrect inference. Under the proportional hazards cure model, we propose a corrected score approach as well as its generalization, and implement a transformation on the mismeasured covariates toward error additivity and/or normality. The corrected…

协变量含测量误差时多项式模型的适用性检验AI 解读

A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general polynomial model when there are errors in the covariates. There, the true covariates are not directly observed, and conventional bootstrap methods for testing are not applicable. We develop a new approach, in which deconvolution methods are used…

未知误差分布下函数型测量误差模型的半参数估计AI 解读

Summary We consider functional measurement error models where the measurement error distribution is estimated non-parametrically. We derive a locally efficient semiparametric estimator but propose not to implement it owing to its numerical complexity. Instead, a plug-in estimator is proposed, where the measurement error distribution is estimated through non-parametric kernel methods based on multiple measurements. The root n consistency and asymptotic normality of the…

一般半参数回归模型中总体汇总量的高效估计AI 解读

This article considers a wide class of semiparametric regression models in which interest focuses on population-level quantities that combine both the parametric and the nonparametric parts of the model. Special cases in this approach include generalized partially linear models, generalized partially linear single-index models, structural measurement error models, and many others. For estimating the parametric part of the model efficiently, profile likelihood kernel…

半参数测量误差模型的局部有效估计量AI 解读

We derive constructive locally efficient estimators in semiparametric measurement error models. The setting is one in which the likelihood function depends on variables measured with and without error, where the variables measured without error can be modeled nonparametrically. The algorithm is based on backfitting. We show that if one adopts a parametric model for the latent variable measured with error and if this model is correct, then the estimator is semiparametric…

异方差部分线性模型的有效半参数估计量AI 解读

We study the heteroscedastic partially linear model with an unspecified partial baseline component and a nonparametric variance function. An interesting finding is that the performance of a naive weighted version of the existing estimator could deteriorate when the smooth baseline component is badly estimated. To avoid this, we propose a family of consistent estimators and investigate their asymptotic properties. We show that the optimal semiparametric efficiency bound can…

广义偏斜椭圆分布的局部有效半参数估计AI 解读

We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model. We show that these estimators are consistent and asymptotically normal. We present the semiparametric efficiency bound and derive the locally efficient estimator that achieves this bound if the model for the skewing function is…