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随机缺失下析因设计的非参数分析AI 解读

We propose a nonparametric approach to the analysis of factorial designs where each subject is observed at two time points and both observations are subject to missingness. The procedures are fully nonparametric in that they do not require continuity, and do not impose models to describe the relation of the response distribution in different factor-level combinations. The approach for estimating and testing treatment and time effects is based on a method, which we introduce,…

通过几何下界推断物种数量AI 解读

Estimating the number of species in a population from a sample of individuals is investigated in a nonparametric Poisson mixture model. A sequence of lower bounds to the odds that a species is unseen in the sample are proposed from a geometric perspective. A lower bound and its representing mixing distribution can be computed by linear programming with guaranteed convergence. These lower bounds can be estimated by the maximum likelihood method and used to construct lower…

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…

马尔可夫链蒙特卡洛的固定宽度输出分析AI 解读

Markov chain Monte Carlo is a method of producing a correlated sample to estimate features of a target distribution through ergodic averages. A fundamental question is when sampling should stop; that is, at what point the ergodic averages are good estimates of the desired quantities. We consider a method that stops the simulation when the width of a confidence interval based on an ergodic average is less than a user-specified value. Hence calculating a Monte Carlo standard…

有限 Pólya 树混合模型的推断AI 解读

Mixtures of Polya tree models provide a flexible alternative when a parametric model may only hold approximately. I provide computational strategies for obtaining full semiparametric inference for mixtures of finite Polya tree models given a standard parameterization, including models that would be troublesome to fit using Dirichlet process mixtures. Recommendations are put forth on choosing the level of a finite Polya tree, and model comparison is discussed. Several…

用 Fourier 方法估计回归的中心子空间与中心均值子空间AI 解读

In regression with a high-dimensional predictor vector, it is important to estimate the central and central mean subspaces that preserve sufficient information about the response and the mean response. Using the Fourier transform, we have derived the candidate matrices whose column spaces recover the central and central mean subspaces exhaustively. Under the normality assumption of the predictors, explicit estimates of the central and central mean subspaces are derived.…

利用倾向得分进行因果推断的分布方法AI 解读

Drawing inferences about the effects of treatments and actions is a common challenge in economics, epidemiology, and other fields. We adopt Rubin's potential outcomes framework for causal inference and propose two methods serving complementary purposes. One can be used to estimate average causal effects, assuming no confounding given measured covariates. The other can be used to assess how the estimates might change under various departures from no confounding. Both methods…

利用工具变量进行因果推断的回归与加权方法AI 解读

Please see the supplementary material for a correction and a new result.Recent researches in econometrics and statistics have gained considerable insights into the use of instrumental variables (IVs) for causal inference. A basic idea is that IVs serve as an experimental handle, the turning of which may change each individual's treatment status and, through and only through this effect, also change observed outcome. The average difference in observed outcome relative to that…

多种生物条件下微阵列时间序列数据的隐马尔可夫模型AI 解读

Among the first microarray experiments were those measuring expression over time, and time course experiments remain common. Most methods to analyze time course data attempt to group genes sharing similar temporal profiles within a single biological condition. However, with time course data in multiple conditions, a main goal is to identify differential expression patterns over time. An intuitive approach to this problem would be to apply at each time point any of the many…

层次 Dirichlet 过程AI 解读

We consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups. We assume that the number of mixture components is unknown a priori and is to be inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one for each group, where the well-known clustering property of the Dirichlet process provides a nonparametric prior…

Cox 风险回归模型的聚焦信息准则与模型平均AI 解读

This article is concerned with variable selection methods for the Cox proportional hazards regression model. Including excessive covariates causes extra variability and inflated confidence intervals for regression parameters; thus regimes for discarding the less informative ones are needed. Our framework has p covariates designated as “protected,” while variables from a further set of q covariates are examined for possible inclusion or exclusion. We develop a focused…

保序逻辑斯蒂判别AI 解读

We propose an isotonic logistic discrimination procedure which generalises linear logistic discrimination by allowing linear boundaries to be more flexibly shaped as monotone functions of the discriminant variables. Under each of three familiar sampling schemes for obtaining a training dataset, namely prospective, mixture and retrospective, we provide the corresponding likelihood-based inference. An application to a cancer study is given. In addition, we consider theoretical…

信息性抽样下的多层模型AI 解读

We consider a model-dependent approach for multi-level modelling that accounts for informative probability sampling of first- and lower-level population units. The proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample, as a function of the corresponding population model and the first- and lower-level sample selection probabilities, and then fitting the resulting sample model using Bayesian methods. An…

标记边际分布的半参数估计AI 解读

In many applications, the outcome of interest is a mark such that its observation is contingent upon occurrence of an event. With incomplete follow-up data, the marginal mark distribution is, however, nonparametrically nowhere identifiable in many practical situations. To address this problem, we suggest a semiparametric model that postulates a normal copula for the association between the mark and survival time, but leaves the marginals unspecified. We show identifiability…

基于狄利克雷过程混合模型的聚类变量选择AI 解读

The increased collection of high-dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures. In this paper, we propose a model-based method that addresses the two problems simultaneously. We introduce a latent binary vector to identify discriminating variables and use Dirichlet process mixture models to define the cluster structure. We update the variable selection index using a Metropolis algorithm and obtain…

Cox 回归模型的后验适定性与计算：缺失协变量应用AI 解读

In this paper, we carry out an in-depth theoretical investigation of Bayesian inference for the Cox regression model. We establish necessary and sufficient conditions for posterior propriety of the regression coefficient, β, in Cox's partial likelihood, which can be obtained as the limiting marginal posterior distribution of β through the specification of a gamma process prior for the cumulative baseline hazard and a uniform improper prior for β. We also examine necessary…

面板计数数据的非参数多样本检验AI 解读

We study the nonparametric k-sample test problem with panel count data. The asymptotic normality of a smooth functional of the nonparametric maximum pseudo-likelihood estimator (Wellner & Zhang, 2000) is established under some mild conditions. We construct a class of easy-to-implement nonparametric tests for comparing mean functions of k populations based on this asymptotic normality. We conduct various simulations to validate and compare the tests. The simulations show that…

病例队列研究中的删失线性回归AI 解读

Right-censored data from a classical case-cohort design and a stratified case-cohort design are considered. In the classical case-cohort design the subcohort is obtained as a simple random sample of the entire cohort, whereas in the stratified design this subcohort is elected by independent Bernoulli sampling with arbitrary selection probabilities. For each design and under a linear regression model, methods for estimating the regression parameters are proposed and analysed.…

广义线性混合模型中混合分布的诊断检验AI 解读

We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimators of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-squared distribution under the null hypothesis that the mixing distribution is correctly specified. This…

基于一类 M 估计量的简便精确单侧推断AI 解读

This paper presents a simple method of calculating one-sided p-values which yield accurate inferences for a simple null hypothesis or, equivalently, accurate one-sided confidence limits regarding a scalar parameter in the presence of nuisance parameters. The method, which extends the work of DiCiccio et al. (2001) and Lee & Young (2005) in the context of adjusted likelihood estimation, is based on a test statistic analogous to the signed root of the loglikelihood, but…

相关结果线性模型的泛函式分布诊断AI 解读

In this paper we present an easy-to-implement graphical distribution diagnostic for linear models with correlated errors. Houseman et al. (2004) constructed quantile–quantile plots for the marginal residuals of such models, suitably transformed. We extend the pointwise asymptotic theory to address the global stochastic behaviour of the corresponding empirical cumulative distribution function, and describe a simulation technique that serves as a computationally efficient…

利用贝叶斯树形捕获再捕获模型构造后分层AI 解读

For the problem of dual system estimation, we propose a Bayesian treed capture-recapture model to account for heterogeneity of capture probabilities where individual auxiliary information is available. The model uses a binary tree to partition the covariate space into ‘homogeneous’ regions, within each of which the capture response can be described adequately by a simple model that assumes equal catchability. The attractive features of the proposed model include reduction of…

作者回复：局部 Rademacher 复杂度与风险最小化中的 oracle 不等式AI 解读

I would like to thank the discussants for a number of deep and interesting comments and for their inspiring work on the subject over the years.I will not be able to address all the issues raised in the discussion; I will concentrate just on several of them. Local complexities and excess risk bounds.The first question is about possible ways to define distribution-and data-dependent complexities (such as local Rademacher complexities).The approach taken in my paper is based on…

高效独立成分分析AI 解读

Independent component analysis (ICA) has been widely used for blind source separation in many fields, such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but in-depth analysis of asymptotic efficiency has not been available. We analyze ICA using semiparametric theories and propose a…