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不可微调查估计量的渐近正态性与方差估计AI 解读

Survey estimators of population quantities such as distribution functions and quantiles contain nondifferentiable functions of estimated quantities. The theoretical properties of such estimators are substantially more complicated to derive than those of differentiable estimators. In this article, we provide a unified framework for obtaining the asymptotic design-based properties of two common types of nondifferentiable estimators. Estimators of the first type have an…

相关性对错误发现率估计的影响AI 解读

The objective of this paper is to quantify the effect of correlation in false discovery rate analysis. Specifically, we derive approximations for the mean, variance, distribution and quantiles of the standard false discovery rate estimator for arbitrarily correlated data. This is achieved using a negative binomial model for the number of false discoveries, where the parameters are found empirically from the data. We show that correlation may increase the bias and variance of…

长度偏倚与右删失数据的非参数估计AI 解读

This paper considers survival data arising from length-biased sampling, where the survival times are left truncated by uniformly distributed random truncation times. We propose a nonparametric estimator that incorporates the information about the length-biased sampling scheme. The new estimator retains the simplicity of the truncation product-limit estimator with a closed-form expression, and has a small efficiency loss compared with the nonparametric maximum likelihood…

三维标志点数据中平均反射形状及大小与形状的自助法推断AI 解读

Working within the framework of a multi-dimensional scaling approach to shape analysis, we develop bootstrap methods for inference about mean reflection shape and size-and-shape based on labelled landmark data. The approach is developed in general dimensions though we focus on the three-dimensional case. We consider two pivotal statistics which we use to construct bootstrap confidence regions for the mean reflection shape or size-and-shape, and present simulation results…

多个图模型的联合估计AI 解读

Gaussian graphical models explore dependence relationships between random variables, through the estimation of the corresponding inverse covariance matrices. In this paper we develop an estimator for such models appropriate for data from several graphical models that share the same variables and some of the dependence structure. In this setting, estimating a single graphical model would mask the underlying heterogeneity, while estimating separate models for each category…

线性时间序列模型相对于门限扩展的检验AI 解读

This paper derives the asymptotic null distribution of a quasilikelihood ratio test statistic for an autoregressive moving average model against its threshold extension. The null hypothesis is that of no threshold, and the error term could be dependent. The asymptotic distribution is rather complicated, and all existing methods for approximating a distribution in the related literature fail to work. Hence, a novel bootstrap approximation based on stochastic permutation is…

状态空间模型中得分与观测信息矩阵的粒子近似及参数估计AI 解读

Particle methods are popular computational tools for Bayesian inference in nonlinear non-Gaussian state space models. For this class of models, we present two particle algorithms to compute the score vector and observed information matrix recursively. The first algorithm is implemented with computational complexity and the second with complexity , where N is the number of particles. Although cheaper, the performance of the method degrades quickly, as it relies on the…

多元贝塔过程与波利亚树模型的扩展AI 解读

We introduce a novel stochastic process that we term the multivariate beta process. The process is defined for modelling-dependent random probabilities and has beta marginal distributions. We use this process to define a probability model for a family of unknown distributions indexed by covariates. The marginal model for each distribution is a Polya tree prior. An important feature of the proposed prior is the easy centring of the nonparametric model around any parametric…

函数型数据的 Horvitz–Thompson 估计：渐近置信带与分层抽样最优配置AI 解读

When dealing with very large datasets of functional data, survey sampling approaches are useful in order to obtain estimators of simple functional quantities, without being obliged to store all the data. We propose a Horvitz–Thompson estimator of the mean trajectory. In the context of a superpopulation framework, we prove, under mild regularity conditions, that we obtain uniformly consistent estimators of the mean function and of its variance function. With additional…

多元线性回归中用于高效估计的部分包络模型AI 解读

We introduce the partial envelope model, which leads to a parsimonious method for multivariate linear regression when some of the predictors are of special interest. It has the potential to achieve massive efficiency gains compared with the standard model in the estimation of the coefficients for the selected predictors. The partial envelope model is a variation on the envelope model proposed by Cook et al. (2010) but, as it focuses on part of the predictors, it has looser…

黎曼流形上的 Langevin 与 Hamiltonian 蒙特卡洛方法AI 解读

Summary The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed…

剂量—反应研究中实验设计的稳健性AI 解读

Summary We construct experimental designs for dose–response studies. The designs are robust against possibly misspecified link functions; for this they minimize the maximum mean-squared error of the estimated dose required to attain a response in 100p% of the target population. Here p might be one particular value—p = 0.5 corresponds to ED50-estimation—or it might range over an interval of values of interest. The maximum of the mean-squared error is evaluated over a…

计数数据的有效概率预测AI 解读

Summary Efficient probabilistic forecasts of integer-valued random variables are derived. The optimality is achieved by estimating the forecast distribution non-parametrically over a given broad model class and proving asymptotic (non-parametric) efficiency in that setting. The method is developed within the context of the integer auto-regressive class of models, which is a suitable class for any count data that can be interpreted as a queue, stock, birth-and-death process…

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…

VIF回归：面向大规模数据的快速回归算法AI 解读

We propose a fast and accurate algorithm, VIF regression, for doing feature selection in large regression problems. VIF regression is extremely fast; it uses a one-pass search over the predictors and a computationally efficient method of testing each potential predictor for addition to the model. VIF regression provably avoids model overfitting, controlling the marginal false discovery rate. Numerical results show that it is much faster than any other published algorithm for…

EEBoost：基于估计方程的预测与变量选择AI 解读

The modern statistical literature is replete with methods for performing variable selection and prediction in standard regression problems. However, simple models may misspecify or fail to capture important aspects of the data generating process such as missingness, correlation, and over/underdispersion. In this article we describe EEBoost, a strategy for variable selection and prediction which can be applied in high-dimensional settings where inference for low-dimensional…

通过检验小区域效应进行模型选择及区域数据应用AI 解读

The models used in small-area inference often involve unobservable random effects. While this can significantly improve the adaptivity and flexibility of a model, it also increases the variability of both point and interval estimators. If we could test for the existence of the random effects, and if the test were to show that they were unlikely to be present, then we would arguably not need to incorporate them into the model, and thus could significantly improve the…

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…

置信分布与元分析的统一框架AI 解读

This article develops a unifying framework, as well as robust meta-analysis approaches, for combining studies from independent sources. The device used in this combination is a confidence distribution (CD), which uses a distribution function, instead of a point (point estimator) or an interval (confidence interval), to estimate a parameter of interest. A CD function contains a wealth of information for inferences, and it is a useful device for combining studies from…

回归模型中的阈值效应检验AI 解读

In this article, we develop a general method for testing threshold effects in regression models, using sup-likelihood-ratio (LR)-type statistics. Although the sup-LR-type test statistic has been considered in the literature, our method for establishing the asymptotic null distribution is new and nonstandard. The standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective…

利用鞍点近似构造小样本半数致死剂量置信区间AI 解读

Confidence intervals for the median lethal dose (LD50) and other dose percentiles in logistic regression models are developed using a generalization of the Fieller theorem for exponential families and saddlepoint approximations. Simulation results show that, in terms of one-tailed and two-tailed coverage, the proposed methodology generally outperforms competing confidence intervals obtained from the classical Fieller, likelihood ratio, and score methods. In terms of…

大型数据集中的快速稳健模型选择AI 解读

Large datasets are increasingly common in many research fields. In particular, in the linear regression context, it is often the case that a huge number of potential covariates are available to explain a response variable, and the first step of a reasonable statistical analysis is to reduce the number of covariates. This can be done in a forward selection procedure that includes selecting the variable to enter, deciding to retain it or stop the selection, and estimating the…

预测变量随机缺失下的非参数回归AI 解读

Nonparametric regression with predictors missing at random (MAR), where the probability of missing depends only on observed variables, is considered. Univariate predictor is the primary case of interest. A new adaptive orthogonal series estimator is developed. Large sample theory shows that the estimator is rate-minimax and it is also sharp-minimax whenever predictors are missing completely at random (MCAR). Furthermore, confidence bands, estimation of nuisance functions,…

半监督加性模型中的传播评分AI 解读

This article presents a semisupervised modeling framework that combines feature-based (x) data and graph-based (G) data for classification/regression of the response Y. In this semisupervised setting, Y is observed for a subset of the observations (labeled) and missing for the remainder (unlabeled). The Propagated Scoring algorithm proposed for fitting this model is a semisupervised fixed-point regularization approach that essentially extends the generalized additive model…