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偏微分方程模型的参数估计AI 解读

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of…

墨西哥无尾蝙蝠鸣声音节：非平稳声学时间序列的贝叶斯函数混合模型AI 解读

We describe a new approach to analyze chirp syllables of free-tailed bats from two regions of Texas in which they are predominant: Austin and College Station. Our goal is to characterize any systematic regional differences in the mating chirps and assess whether individual bats have signature chirps. The data are analyzed by modeling spectrograms of the chirps as responses in a Bayesian functional mixed model. Given the variable chirp lengths, we compute the spectrograms on…

病例对照数据二次分析中同方差回归的稳健估计AI 解读

Summary Primary analysis of case–control studies focuses on the relationship between disease D and a set of covariates of interest (Y, X). A secondary application of the case–control study, which is often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated owing to the case–control sampling, where the regression of Y on X is different from what it is in the population.…

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…

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…

广义可加部分线性模型的估计与变量选择AI 解读

We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of…

测量误差下形状约束非参数密度与回归的检验和估计AI 解读

In many applications we can expect that, or are interested to know if, a density function or a regression curve satisfies some specific shape constraints. For example, when the explanatory variable, X, represents the value taken by a treatment or dosage, the conditional mean of the response, Y , is often anticipated to be a monotone function of X. Indeed, if this regression mean is not monotone (in the appropriate direction) then the medical or commercial value of the…

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…

含半参数单指标交互的广义函数型线性模型AI 解读

We introduce a new class of functional generalized linear models, where the response is a scalar and some of the covariates are functional. We assume that the response depends on multiple covariates, a finite number of latent features in the functional predictor, and interaction between the two. To achieve parsimony, the interaction between the multiple covariates and the functional predictor is modeled semiparametrically with a single-index structure. We propose a two step…

空间相关层级函数数据的降秩混合效应模型AI 解读

Hierarchical functional data are widely seen in complex studies where sub-units are nested within units, which in turn are nested within treatment groups. We propose a general framework of functional mixed effects model for such data: within unit and within sub-unit variations are modeled through two separate sets of principal components; the sub-unit level functions are allowed to be correlated. Penalized splines are used to model both the mean functions and the principal…

分析纵向数据的广义经验似然方法AI 解读

Abstract Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood-based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks theorem for the limiting distributions of the empirical likelihood ratios is derived. It is shown that one of the proposed methods is locally efficient among a class of within-subject variance-covariance matrices. A…

测量误差模型中的非参数预测AI 解读

Predicting the value of a variable Y corresponding to a future value of an explanatory variable X, based on a sample of previously observed independent data pairs (X(1), Y(1)), …, (X(n), Y(n)) distributed like (X, Y), is very important in statistics. In the error-free case, where X is observed accurately, this problem is strongly related to that of standard regression estimation, since prediction of Y can be achieved via estimation of the regression curve E(Y|X). When the…

含测量误差的分位数回归AI 解读

Regression quantiles can be substantially biased when the covariates are measured with error. In this paper we propose a new method that produces consistent linear quantile estimation in the presence of covariate measurement error. The method corrects the measurement error induced bias by constructing joint estimating equations that simultaneously hold for all the quantile levels. An iterative EM-type estimation algorithm to obtain the solutions to such joint estimation…

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…

单倍型病例对照研究中兼顾稳健性与效率的收缩估计AI 解读

Case-control association studies often aim to investigate the role of genes and gene-environment interactions in terms of the underlying haplotypes (i.e., the combinations of alleles at multiple genetic loci along chromosomal regions). The goal of this article is to develop robust but efficient approaches to the estimation of disease odds-ratio parameters associated with haplotypes and haplotype-environment interactions. We consider "shrinkage" estimation techniques that can…

变量含测量误差问题中适应设计分布的局部多项式估计AI 解读

Local polynomial estimators are popular techniques for nonparametric regression estimation and have received great attention in the literature. Their simplest version, the local constant estimator, can be easily extended to the errors-in-variables context by exploiting its similarity with the deconvolution kernel density estimator. The generalization of the higher order versions of the estimator, however, is not straightforward and has remained an open problem for the last…

含交互作用的半参数模型检验及基因—环境交互应用AI 解读

Summary Motivated from the problem of testing for genetic effects on complex traits in the presence of gene–environment interaction, we develop score tests in general semiparametric regression problems that involves Tukey style 1 degree-of-freedom form of interaction between parametrically and non-parametrically modelled covariates. We find that the score test in this type of model, as recently developed by Chatterjee and co-workers in the fully parametric setting, is biased…

固定效应面板模型的非参数估计与检验AI 解读

In this paper we consider the problem of estimating nonparametric panel data models with fixed effects. We introduce an iterative nonparametric kernel estimator. We also extend the estimation method to the case of a semiparametric partially linear fixed effects model. To determine whether a parametric, semiparametric or nonparametric model is appropriate, we propose test statistics to test between the three alternatives in practice. We further propose a test statistic for…

Berkson 与经典测量误差混合污染下的非参数回归估计AI 解读

Summary Estimation of a regression function is a well-known problem in the context of errors in variables, where the explanatory variable is observed with random noise. This noise can be of two types, which are known as classical or Berkson, and it is common to assume that the error is purely of one of these two types. In practice, however, there are many situations where the explanatory variable is contaminated by a mixture of the two errors. In such instances, the Berkson…

纵向与空间数据相关函数的非参数估计及结肠致癌实验应用AI 解读

In longitudinal and spatial studies, observations often demonstrate strong correlations that are stationary in time or distance lags, and the times or locations of these data being sampled may not be homogeneous. We propose a nonparametric estimator of the correlation function in such data, using kernel methods. We develop a pointwise asymptotic normal distribution for the proposed estimator, when the number of subjects is fixed and the number of vectors or functions within…

关于条件生长曲线方法的讨论AI 解读

Overview.Wei and He are to be congratulated on an innovative and important article.The conditional approach to growth charts described in their article is important in a practical sense, and the use of quantile regression is both natural and well motivated.We look forward to further application of their idea to actual practice, because the concept of "falling behind" in one's growth cycle has two meanings: the usual standard growth chart, and the conditional growth chart…

基于小波的函数型混合模型AI 解读

Summary Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects…

一般重复测量问题中的半参数估计AI 解读

Summary The paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function. Special cases in our approach include marginal models for longitudinal or clustered data, conditional logistic regression for matched case–control studies, multivariate measurement error models, generalized linear mixed models with a semiparametric component, and many others. We propose profile kernel and…

利用基因与环境独立性的病例对照半参数最大似然估计AI 解读

We consider the problem of maximum-likelihood estimation in case-control studies of gene-environment associations with disease when genetic and environmental exposures can be assumed to be independent in the underlying population. Traditional logistic regression analysis may not be efficient in this setting. We study the semiparametric maximum likelihood estimates of logistic regression parameters that exploit the gene-environment independence assumption and leave the…