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半参数模型的最优区分设计AI 解读

Much work on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters. Recent work allows errors in the models to be nonnormally distributed but still requires the specification of the mean structures. Otsu (2008) proposed optimal discriminating designs for semiparametric models by generalizing the Kullback–Leibler optimality criterion proposed by López-Fidalgo et al. (2007). This paper develops a relatively simple…

结构工具变量模型的两阶段估计AI 解读

Two-stage least squares estimation is popular for structural equation models with unmeasured confounders. In such models, both the outcome and the exposure are assumed to follow linear models conditional on the measured confounders and instrumental variable, which is related to the outcome only via its relation with the exposure. We consider data where both the outcome and the exposure may be incompletely observed, with particular attention to the case where both are…

粒子Gibbs采样器的分块策略与稳定性AI 解读

Sampling from the posterior probability distribution of the latent states of a hidden Markov model is nontrivial even in the context of Markov chain Monte Carlo. To address this, Andrieu et al. (2010) proposed a way of using a particle filter to construct a Markov kernel that leaves the posterior distribution invariant. Recent theoretical results have established the uniform ergodicity of this Markov kernel and shown that the mixing rate does not deteriorate provided the…

平均处理效应的双重稳健非参数推断AI 解读

Summary Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average…

基于 lasso 惩罚 D-trace 损失的差异网络分析AI 解读

Biological networks often change under different environmental and genetic conditions. In this paper, we model network change as the difference of two precision matrices and propose a novel loss function called the D-trace loss, which allows us to directly estimate the precision matrix difference without attempting to estimate the precision matrices themselves. Under a new irrepresentability condition, we show that the D-trace loss function with the lasso penalty can yield…

疗效与毒性结局下活性对照剂量探索试验的最优设计AI 解读

We derive optimal designs to estimate efficacy and toxicity in active controlled dose-finding trials when the bivariate continuous outcomes are described using nonlinear regression models. We determine upper bounds on the required number of different doses and provide conditions under which the boundary points of the design space are included in the optimal design. We provide an analytical description of minimally supported optimal designs and show that they do not depend on…

半参数因果推断中的 Cp 模型选择准则AI 解读

Summary For marginal structural models, which play an important role in causal inference, we consider a model selection problem within a semiparametric framework using inverse-probability-weighted estimation or doubly robust estimation. In this framework, the modelling target is a potential outcome that may be missing, so there is no classical information criterion. We define a mean squared error for treating the potential outcome and derive an asymptotic unbiased estimator…

基于分组的超高维变量筛选AI 解读

Traditional variable selection methods are compromised by overlooking useful information on covariates with similar functionality or spatial proximity, and by treating each covariate independently. Leveraging prior grouping information on covariates, we propose partition-based screening methods for ultrahigh-dimensional variables in the framework of generalized linear models. We show that partition-based screening exhibits the sure screening property with a vanishing false…

高维情形下的分布无关独立性检验AI 解读

We consider the testing of mutual independence among all entries in a $d$-dimensional random vector based on $n$ independent observations. We study two families of distribution-free test statistics, which include Kendall’s tau and Spearman’s rho as important examples. We show that under the null hypothesis the test statistics of these two families converge weakly to Gumbel distributions, and we propose tests that control the Type I error in the high-dimensional setting where…

系统发育树空间中的主成分分析与 Fréchet 均值轨迹AI 解读

Evolutionary relationships are represented by phylogenetic trees, and a phylogenetic analysis of gene sequences typically produces a collection of these trees, one for each gene in the analysis. Analysis of samples of trees is difficult due to the multi-dimensionality of the space of possible trees. In Euclidean spaces, principal component analysis is a popular method of reducing high-dimensional data to a low-dimensional representation that preserves much of the sample’s…

病例对照研究中复杂多基因与环境交互作用的半参数分析AI 解读

Many methods have recently been proposed for efficient analysis of case-control studies of gene-environment interactions using a retrospective likelihood framework that exploits the natural assumption of gene-environment independence in the underlying population. However, for polygenic modelling of gene-environment interactions, which is a topic of increasing scientific interest, applications of retrospective methods have been limited due to a requirement in the literature…

通过邻域平滑估计网络连边概率AI 解读

Summary The estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the…

贝叶斯局部极值样条AI 解读

Summary We consider shape-restricted nonparametric regression on a closed set $\mathcal{X} \subset \mathbb{R},$ where it is reasonable to assume that the function has no more than $H$ local extrema interior to $\mathcal{X}$. Following a Bayesian approach we develop a nonparametric prior over a novel class of local extremum splines. This approach is shown to be consistent when modelling any continuously differentiable function within the class considered, and we use itto…

最大似然估计的中位数偏差校正AI 解读

For regular parametric problems, we show how median centring of the maximum likelihood estimate can be achieved by a simple modification of the score equation. For a scalar parameter of interest, the estimator is equivariant under interest-respecting reparameterizations and is third-order median unbiased. With a vector parameter of interest, componentwise equivariance and third-order median centring are obtained. Like the implicit method of Firth (1993) for bias reduction,…

两个随机向量之间的投影相关AI 解读

We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We…

具有依赖结构的广义函数型线性模型AI 解读

This paper considers testing for no effect of functional covariates on response variables in multivariate regression. We use generalized estimating equations to determine the underlying parameters and establish their joint asymptotic normality. This is then used to test the significance of the effect of predictors on the vector of response variables. Simulations demonstrate the importance of considering existing correlation structures in the data. To explore the effect of…

组稀疏性下的不确定性量化AI 解读

Quantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons,…

具有尖峰—连续混合基测度的 Pitman–Yor 过程AI 解读

Summary For the most popular discrete nonparametric models, beyond the Dirichlet process, the prior guess at the shape of the data-generating distribution, also known as the base measure, is assumed to be diffuse. Such a specification greatly simplifies the derivation of analytical results, allowing for a straightforward implementation of Bayesian nonparametric inferential procedures. However, in several applied problems the available prior information leads naturally to the…

多元区间删失数据半参数回归模型的最大似然估计AI 解读

Interval-censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval. We investigate the effects of possibly time-dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects, and we study nonparametric maximum likelihood estimation under general interval-censoring…

稳健降秩回归AI 解读

Summary In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly used reduced-rank methods are sensitive to data corruption, as the low-rank dependence structure between response variables and predictors is easily distorted by outliers. We propose a robust reduced-rank regression approach for joint…

死亡截断结局下因果效应的识别与估计AI 解读

It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification…

简单、可扩展且准确的后验区间估计AI 解读

Summary Standard posterior sampling algorithms, such as Markov chain Monte Carlo procedures, face major challenges in scaling up to massive datasets. We propose a simple and general posterior interval estimation algorithm to rapidly and accurately estimate quantiles of the posterior distributions for one-dimensional functionals. Our algorithm runs Markov chain Monte Carlo in parallel for subsets of the data, and then averages quantiles estimated from each subset. We provide…

利用无偏估计量平均值的伪边际 Metropolis–Hastings 抽样AI 解读

Summary We consider a pseudo-marginal Metropolis–Hastings kernel ${\mathbb{P}}_m$ that is constructed using an average of $m$ exchangeable random variables, and an analogous kernel ${\mathbb{P}}_s$ that averages $s<m$ of these same random variables. Using an embedding technique to facilitate comparisons, we provide a lower bound for the asymptotic variance of any ergodic average associated with ${\mathbb{P}}_m$ in terms of the asymptotic variance of the corresponding ergodic…

可扩展因子分析AI 解读

Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable inference in factor models when the number of factors is unknown. The method relies on a continuous shrinkage prior for efficient maximum a posteriori estimation of a low-rank and sparse loadings matrix. The structure of the prior leads to an…