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Bagging 的理论分析AI 解读

Bagging is one of the most effective computationally intensive procedures to improve on unstable estimators or classifiers, useful especially for high dimensional data set problems. Here we formalize the notion of instability and derive theoretical results to analyze the variance reduction effect of bagging (or variants thereof) in mainly hard decision problems, which include estimation after testing in regression and decision trees for regression functions and classifiers.…

用信息准则选择协整秩与截距形式AI 解读

In this paper we consider a family of penalized likelihood criteria for determining the rank of the cointegration space, the number of lags, and the form of the intercept in vector autoregressions with possibly integrated processes. The paper provides a general consistency result for a class of model determination procedures in which the penalty depends on a simple parameter count only.

线性回归中的变量选择AI 解读

Shibata (1981, Biometrika 68, 45–54) considers data-generating mechanisms belonging to a certain class of linear regressions with errors that are independent and identically normally distributed. He compares the variable selection criteria AIC (Akaike information criterion) and BIC (Bayesian information criterion) using the following type of comparison. For each fixed possible data–generating mechanism, these criteria are compared as the data length increases. The results of…

高维情形下分布相等性的置换检验AI 解读

Motivated by applications in high‐dimensional settings, we suggest a test of the hypothesis H0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may be multivariate or infinite‐dimensional, in the latter case representing, for example, the distributions of random functions from one Euclidean space to another. Our test uses a measure…

与表型相关的基因区域异质性非参数检验AI 解读

High-dimensional statistical problems arise in the investigation of the relationship between reduced sensitivity to antiretroviral drugs among human immunodeficiency virus-infected patients and viral genotypic patterns obtained from blood samples. This article develops a nonparametric approach for analyzing gene region heterogeneity associated with drug-resistance phenotype. The method is based on the distribution of distances between viral genetic sequences. The distance…

基于模型的聚类、判别分析与密度估计AI 解读

Cluster analysis is the automated search for groups of related observations in a dataset. Most clustering done in practice is based largely on heuristic but intuitively reasonable procedures, and most clustering methods available in commercial software are also of this type. However, there is little systematic guidance associated with these methods for solving important practical questions that arise in cluster analysis, such as how many clusters are there, which clustering…

纵向边际模型中的非参数回归AI 解读

We consider nonparametric regression in a longitudinal marginal model of generalized estimating equation (GEE) type with a time-varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large. In such models, the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations. Two methods of estimating the nonparametric function can be…

复杂区域上的样条平滑AI 解读

Summary It is occasionally necessary to smooth data over domains in ℝ2 with complex irregular boundaries or interior holes. Traditional methods of smoothing which rely on the Euclidean metric or which measure smoothness over the entire real plane may then be inappropriate. This paper introduces a bivariate spline smoothing function defined as the minimizer of a penalized sum-of-squares functional. The roughness penalty is based on a partial differential operator and is…

含类别预测变量的回归充分降维AI 解读

In this article, we describe how the theory of sufficient dimension reduction, and a well-known inference method for it (sliced inverse regression), can be extended to regression analyses involving both quantitative and categorical predictor variables. As statistics faces an increasing need for effective analysis strategies for high-dimensional data, the results we present significantly widen the applicative scope of sufficient dimension reduction and open the way for a new…

面板计数数据的半参数伪似然估计方法AI 解读

In this paper, we study panel count data with covariates. A semiparametric pseudolikelihood estimation method is proposed based on the assumption that, given a covariate vector Z, the underlying counting process is a nonhomogeneous Poisson process with the conditional mean function given by E{N (t) |Z} = Λ0 (t) exp (β′0Z). The proposed estimation method is shown to be robust in the sense that the estimator converges to its true value regardless of whether or not N (t) is a…

自适应模型选择AI 解读

Most model selection procedures use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for “small” models and poorly for “large” models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity…

高崩溃点回归估计重抽样算法的不一致性与一种新算法AI 解读

Because high-breakdown estimators (HBEs) are impractical to compute exactly in large samples, approximate algorithms are used. The algorithm generally produces an estimator with a lower consistency rate and breakdown value than the exact theoretical estimator. This discrepancy grows with the sample size, with the implication that huge computations are needed for good approximations in large high-dimension samples. The workhorse for HBEs has been the “elemental set,” or…

Cox 比例风险模型与脆弱性模型的变量选择AI 解读

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed in Fan and Li (2001a). It has been shown there that the resulting procedures perform as well as if the subset of significant variables were known in advance. Such a property is called an oracle property. The proposed procedures were illustrated in the context of linear regression, robust linear regression and generalized linear models. In this paper, the nonconcave…

弱基假设及其对提升回归与分类的含义AI 解读

When studying the training error and the prediction error for boosting, it is often assumed that the hypotheses returned by the base learner are weakly accurate, or are able to beat a random guesser by a certain amount of difference. It has been an open question how much this difference can be, whether it will eventually disappear in the boosting process or be bounded by a positive amount. This question is crucial for the behavior of both the training error and the…

This paper considers causal inference and sample selection bias in nonexperimental settings in which (i) few units in the nonexperimental comparison group are comparable to the treatment units, and (ii) selecting a subset of comparison units similar to the treatment units is difficult because units must be compared across a high-dimensional set of pretreatment characteristics. We discuss the use of propensity score-matching methods, and implement them using data from the…

病例对照数据逻辑回归模型的信息矩阵检验AI 解读

We propose an information‐matrix‐based goodness‐of‐fit statistic to test the validity of the logistic regression model based on case‐control data by extending the information matrix test of White (1982) for detecting one‐sample parametric model misspecification to the semiparametric profile likelihood setting under a two‐sample semiparametric model, which is equivalent to the assumed logistic regression model. The proposed test statistic requires a high‐dimensional matrix…

无限参数线性回归中的自适应预测与估计AI 解读

The problem of adaptive prediction and estimation in the stochastic linear regression model with infinitely many parameters is considered.We suggest a prediction method that is sharp asymptotically minimax adaptive over ellipsoids in $\ell_2$. The method consists in an application of blockwise Stein’s rule with “weakly” geometrically increasing blocks to the penalized least squares fits of the first $N$ coefficients. To prove the results we develop oracle inequalities for a…

半参数非线性混合效应模型及其应用AI 解读

Nonlinear mixed effects models (NLMMs) and self-modeling nonlinear regression (SEMOR) models are often used to fit repeated measures data. They use a common function shared by all subjects to model variation within each subject and some fixed and/or random parameters to model variation between subjects. The parametric NLMM may be too restrictive, and the semiparametric SEMOR model ignores correlations within each subject. In this article we propose a class of semiparametric…

群组随机试验分析的最优置换检验AI 解读

Two facts complicate the comparison of interventions in group randomized trials (GRT's), a family of clinical trials in which each member of a particular group receives the same treatment assignment. First, individual outcomes within each group are often correlated. Second, the number of groups in a GRT is often not sufficient to make asymptotic approximations possible. Therefore, the tests used with methods, such as generalized estimating equations (GEE) and penalized quasi…

非凹惩罚似然变量选择及其 Oracle 性质AI 解读

Variable selection is fundamental to high-dimensional statistical modeling, including nonparametric regression. Many approaches in use are stepwise selection procedures, which can be computationally expensive and ignore stochastic errors in the variable selection process. In this article, penalized likelihood approaches are proposed to handle these kinds of problems. The proposed methods select variables and estimate coefficients simultaneously. Hence they enable us to…

树结构广义自回归条件异方差模型AI 解读

Summary We propose a new generalized autoregressive conditional heteroscedastic (GARCH) model with tree-structured multiple thresholds for the estimation of volatility in financial time series. The approach relies on the idea of a binary tree where every terminal node parameterizes a (local) GARCH model for a partition cell of the predictor space. The fitting of such trees is constructed within the likelihood framework for non-Gaussian observations: it is very different from…

神经网络中的贝叶斯推断AI 解读

Approximate marginal Bayesian computation and inference are developed for neural network models. The marginal considerations include determination of approximate Bayes factors for model choice about the number of nonlinear sigmoid terms, approximate predictive density computation for a future observable and determination of approximate Bayes estimates for the nonlinear regression function. Standard conjugate analysis applied to the linear parameters leads to an explicit…

分数高斯过程的惩罚极大似然估计AI 解读

We apply and extend Firth's (1993) modified score estimator to deal with a class of stationary Gaussian long‐memory processes. Our estimator removes the first‐order bias of the maximum likelihood estimator. A small simulation study reveals the reduction in the bias is considerable, while it does not inflate the corresponding mean squared error.

贪婪函数逼近：梯度提升机AI 解读

Function estimation/approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent “boosting” paradigm is developed for additive expansions based on any fitting criterion.Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and…