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客观贝叶斯变量选择AI 解读

A novel fully automatic Bayesian procedure for variable selection in normal regression models is proposed. The procedure uses the posterior probabilities of the models to drive a stochastic search. The posterior probabilities are computed using intrinsic priors, which can be considered default priors for model selection problems; that is, they are derived from the model structure and are free from tuning parameters. Thus they can be seen as objective priors for variable…

基于模型的聚类中的变量选择AI 解读

We consider the problem of variable or feature selection for model-based clustering. The problem of comparing two nested subsets of variables is recast as a model comparison problem and addressed using approximate Bayes factors. A greedy search algorithm is proposed for finding a local optimum in model space. The resulting method selects variables (or features), the number of clusters, and the clustering model simultaneously. We applied the method to several simulated and…

凸性、分类与风险界AI 解读

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general…

分组变量回归中的模型选择与估计AI 解读

Summary We consider the problem of selecting grouped variables (factors) for accurate prediction in regression. Such a problem arises naturally in many practical situations with the multifactor analysis-of-variance problem as the most important and well-known example. Instead of selecting factors by stepwise backward elimination, we focus on the accuracy of estimation and consider extensions of the lasso, the LARS algorithm and the non-negative garrotte for factor selection.…

函数主成分分析的惩罚样条模型AI 解读

Summary We propose an iterative estimation procedure for performing functional principal component analysis. The procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated. An increasingly popular smoothing approach, penalized spline regression, is used to represent the mean function. This allows straightforward incorporation of covariates and simple implementation of approximate inference procedures for…

生存时间数据的局部部分似然估计AI 解读

This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partial-likelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of the proposed estimator is established. The baseline hazard function, the bias and the variance of the local likelihood estimator are consistently estimated. In addition, a one-step…

惩罚最大似然与半参数二阶效率AI 解读

We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the…

收缩型估计量风险与分布估计的性能限制及一般风险下界AI 解读

We consider the problem of estimating measures of precision of shrinkage-type estimators such as their risk or distribution. The notion of shrinkage-type estimators here refers to estimators such as the James–Stein estimator and Lasso-type estimators, in addition to “thresholding” estimators such as, e.g., Hodges' so-called superefficient estimator. Although the precision measures of such estimators typically can be estimated consistently, we show that they cannot be…

贝叶斯变量选择的自适应抽样AI 解读

Our paper proposes adaptive Monte Carlo sampling schemes for Bayesian variable selection in linear regression that improve on standard Markov chain methods. We do so by considering Metropolis–Hastings proposals that make use of accumulated information about the posterior distribution obtained during sampling. Adaptation needs to be done carefully to ensure that sampling is from the correct ergodic distribution. We give conditions for the validity of an adaptive sampling…

复杂调查中基于惩罚样条的模型辅助估计AI 解读

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalised spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. They allow straightforward extensions to multiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically…

线性模型中的高效经验贝叶斯变量选择与估计AI 解读

We propose an empirical Bayes method for variable selection and coefficient estimation in linear regression models. The method is based on a particular hierarchical Bayes formulation, and the empirical Bayes estimator is shown to be closely related to the LASSO estimator. Such a connection allows us to take advantage of the recently developed quick LASSO algorithm to compute the empirical Bayes estimate, and provides a new way to select the tuning parameter in the LASSO…

线性回归中对离群值稳健的模型选择AI 解读

We propose a new approach to the selection of regression models based on combining a robust penalized criterion and a robust conditional expected prediction loss function that is estimated using a stratified bootstrap. Both components of the procedure use robust criteria (i.e., robust ρ-functions) rather than squared error loss to reduce the effects of large residuals and poor bootstrap samples. A key idea is to separate estimation from model selection by choosing estimators…

调查抽样中的非参数模型校准估计AI 解读

Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on population means (totals) of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean (total). Implicitly, calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary…

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现时状态数据下部分线性变换模型的惩罚对数似然估计AI 解读

We consider partly linear transformation models applied to current status data. The unknown quantities are the transformation function, a linear regression parameter and a nonparametric regression effect. It is shown that the penalized MLE for the regression parameter is asymptotically normal and efficient and converges at the parametric rate, although the penalized MLE for the transformation function and nonparametric regression effect are only n1/3 consistent. Inference…

多元正态混合分布的地形结构AI 解读

Multivariate normal mixtures provide a flexible method of fitting high-dimensional data. It is shown that their topography, in the sense of their key features as a density, can be analyzed rigorously in lower dimensions by use of a ridgeline manifold that contains all critical points, as well as the ridges of the density. A plot of the elevations on the ridgeline shows the key features of the mixed density. In addition, by use of the ridgeline, we uncover a function that…

利用泊松方差结构分析亡故供者肾移植数据的脆弱性生存模型AI 解读

In a recent study of transplant outcomes, donor age, cerebrovascular accident as the cause of death (CVA), renal insufficiency (serum creatinine >1.5 mg/dL), and history of hypertension have been identified as donor factors associated with elevated risk of kidney transplant failure. It is of great interest to know whether there remain other unmeasured donor factors associated with elevated risk of graft failure. In this article we study a sample of 6,024 deceased donor…

物种丰富度估计的惩罚非参数最大似然方法AI 解读

We propose a class of penalized nonparametric maximum likelihood estimators (NPMLEs) for the species richness problem. We use a penalty term on the likelihood because likelihood estimators that lack it have an extreme instability problem. The estimators are constructed using a conditional likelihood that is simpler than the full likelihood. We show that the full-likelihood NPMLE solution given by Norris and Pollock can be found (with great accuracy) by using an appropriate…

微阵列数据归一化的半线性高维模型AI 解读

Normalization of microarray data is essential for removing experimental biases and revealing meaningful biological results. Motivated by a problem of normalizing microarray data, a semilinear in-slide model (SLIM) has been proposed. To aggregate information from other arrays, SLIM is generalized to account for across-array information, resulting in an even more dynamic semiparametric regression model. This model can be used to normalize microarray data even when there is no…

高维二元列联表的有限信息与完全信息估计及拟合优度检验AI 解读

High-dimensional contingency tables tend to be sparse, and standard goodness-of-fit statistics such as X2 cannot be used without pooling categories. As an improvement on arbitrary pooling, for goodness of fit of large 2n contingency tables, we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r. These classes of test statistics are asymptotically chi-squared distributed under the null hypothesis. Further, the…

一类新的广义贝叶斯极小极大岭回归估计量AI 解读

Let y=Aβ+ɛ, where y is an N×1 vector of observations, β is a p×1 vector of unknown regression coefficients, A is an N×p design matrix and ɛ is a spherically symmetric error term with unknown scale parameter σ. We consider estimation of β under general quadratic loss functions, and, in particular, extend the work of Strawderman [J. Amer. Statist. Assoc. 73 (1978) 623–627] and Casella [Ann. Statist. 8 (1980) 1036–1056, J. Amer. Statist. Assoc. 80 (1985) 753–758] by finding…

高维球面与形状空间上的统计分析AI 解读

We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available—a commonly encountered situation in many disciplines. First the uniform measure on the infinite-dimensional sphere is reviewed, together with connections with Wiener measure. We then discuss densities of Gaussian measures with respect to Wiener measure. Some nonuniform distributions on…

Boosting is one of the most significant advances in machine learning for classification and regression. In its original and computationally flexible version, boosting seeks to minimize empirically a loss function in a greedy fashion. The resulting estimator takes an additive function form and is built iteratively by applying a base estimator (or learner) to updated samples depending on the previous iterations. An unusual regularization technique, early stopping, is employed…

使用 MM 算法进行变量选择AI 解读

Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function is often challenging because it may be nondifferentiable and/or nonconcave. This article proposes a new class of algorithms for finding a maximizer of the penalized likelihood for a broad class of penalty functions. These algorithms…