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高维小样本的几何表示在较弱条件下成立AI 解读

High-dimension, low-small-sample size datasets have different geometrical properties from those of traditional low-dimensional data. In their asymptotic study regarding increasing dimensionality with a fixed sample size, Hall et al. (2005) showed that each data vector is approximately located on the vertices of a regular simplex in a high-dimensional space. A perhaps unappealing aspect of their result is the underlying assumption which requires the variables, viewed as a…

Cox 比例风险模型的自适应 LassoAI 解读

We investigate the variable selection problem for Cox's proportional hazards model, and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience. The new method is based on a penalized log partial likelihood with the adaptively weighted L1 penalty on regression coefficients, providing what we call the adaptive Lasso estimator. The method incorporates different penalties for different coefficients:…

Bayesian variable selection has gained much empirical success recently in a variety of applications when the number K of explanatory variables $(x_1,\ldots,x_K)$ is possibly much larger than the sample size $n$. For generalized linear models, if most of the $x_j$’s have very small effects on the response $y$, we show that it is possible to use Bayesian variable selection to reduce overfitting caused by the curse of dimensionality $K\gg n$. In this approach a suitable prior…

高斯回归中的聚合AI 解读

This paper studies statistical aggregation procedures in the regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of aggregation: model selection (MS) aggregation, convex (C) aggregation and linear (L) aggregation. The objective of (MS) is to select the optimal single estimator from the list; that of (C) is to select the optimal convex combination of…

“大维度、小样本”范式的边际渐近理论及微阵列应用AI 解读

The “large $p$, small $n$” paradigm arises in microarray studies, image analysis, high throughput molecular screening, astronomy, and in many other high dimensional applications. False discovery rate (FDR) methods are useful for resolving the accompanying multiple testing problems. In cDNA microarray studies, for example, $p$-values may be computed for each of $p$ genes using data from $n$ arrays, where typically $p$ is in the thousands and $n$ is less than 30. For FDR…

一种适用于S估计的模型选择方法AI 解读

Cleaning data or removing some data periods in least squares (LS) regression analysis is not unusual. This practice indicates that a researcher sometimes desires to estimate the parameter value, with which the regression function fits a large fraction of individuals or events in the population (behind the original data set), possibly exhibiting poor fits to some atypical individuals or events. The S-estimators are a class of estimators that are consistent with the…

摘要暂缺

通过 LAD-lasso 实现稳健回归收缩与一致变量选择AI 解读

The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso) is a popular choice for shrinkage estimation and variable selection. In this article we combine these two classical ideas together to produce LAD-lasso. Compared with the LAD regression, LAD-lasso can do parameter estimation and variable selection simultaneously. Compared with the traditional lasso, LAD-lasso is resistant to…

基于系数符号预测的模型选择方法AI 解读

Summary We consider a Bayesian model selection strategy based on predicting the signs of the coefficients in a regression model, i.e. we consider identification of coefficients in a full or encompassing model for which we can confidently predict whether they are positive or negative. This is useful when our main purpose in doing model selection is interpretation, since the sign of a coefficient is often of primary importance for this task. In the case of a linear model with…

多元线性回归中的降维与系数估计AI 解读

Summary We introduce a general formulation for dimension reduction and coefficient estimation in the multivariate linear model. We argue that many of the existing methods that are commonly used in practice can be formulated in this framework and have various restrictions. We continue to propose a new method that is more flexible and more generally applicable. The method proposed can be formulated as a novel penalized least squares estimate. The penalty that we employ is the…

存在不依从且结局为二元变量的随机试验中治疗效应的估计AI 解读

Summary We propose a class of estimators of the treatment effect on a dichotomous outcome among the treated subjects within covariate and treatment arm strata in randomized trials with non-compliance. Recent papers by Vansteelandt and Goetghebeur, and Robins and Rotnitzky have presented consistent and asymptotically linear estimators of a causal odds ratio, which rely, beyond correct specification of a model for the causal odds ratio, on a correctly specified model for a…

L1范数多分类支持向量机AI 解读

Binary support vector machines (SVMs) have been proven to deliver high performance. In multiclass classification, however, issues remain with respect to variable selection. One challenging issue is classification and variable selection in the presence of variables in the magnitude of thousands, greatly exceeding the size of training sample. This often occurs in genomics classification. To meet the challenge, this article proposes a novel multiclass support vector machine,…

空间贝叶斯变量选择及其在功能磁共振成像中的应用AI 解读

We propose a procedure to undertake Bayesian variable selection and model averaging for a series of regressions located on a lattice. For those regressors that are in common in the regressions, we consider using an Ising prior to smooth spatially the indicator variables representing whether or not the variable is zero or nonzero in each regression. This smooths spatially the probabilities that each independent variable is nonzero in each regression and indirectly smooths…

约束统计推断中的高维小样本视角AI 解读

High-dimensional categorical data models, often with inadequately large sample sizes, crop up in many fields of application. The SARS epidemic, originating in southern China in 2002, had an identified single-stranded and positive-sense RNA virus with large genome size and moderate mutation rate. The present genomic study is used as a prime illustration for motivating appropriate statistical methodology for comprehending the genomic variation in such high-dimensional…

非负Garrotte估计量研究AI 解读

Summary We study the non-negative garrotte estimator from three different aspects: consistency, computation and flexibility. We argue that the non-negative garrotte is a general procedure that can be used in combination with estimators other than the original least squares estimator as in its original form. In particular, we consider using the lasso, the elastic net and ridge regression along with ordinary least squares as the initial estimate in the non-negative garrotte.…

再生核希尔伯特空间中的分位数回归AI 解读

In this article we consider quantile regression in reproducing kernel Hilbert spaces, which we call kernel quantile regression (KQR). We make three contributions: (1) we propose an efficient algorithm that computes the entire solution path of the KQR, with essentially the same computational cost as fitting one KQR model; (2) we derive a simple formula for the effective dimension of the KQR model, which allows convenient selection of the regularization parameter; and (3) we…

通过添加伪变量控制变量选择AI 解读

We propose a new approach to variable selection designed to control the false selection rate (FSR), defined as the proportion of uninformative variables included in selected models. The method works by adding a known number of pseudovariables to the real dataset, running a variable selection procedure, and monitoring the proportion of pseudovariables falsely selected. Information obtained from bootstrap-like replications of this process is used to estimate the proportion of…

高斯图模型中的模型选择与估计AI 解读

We propose penalized likelihood methods for estimating the concentration matrix in the Gaussian graphical model. The methods lead to a sparse and shrinkage estimator of the concentration matrix that is positive definite, and thus conduct model selection and estimation simultaneously. The implementation of the methods is nontrivial because of the positive definite constraint on the concentration matrix, but we show that the computation can be done effectively by taking…

单指标模型的变量选择AI 解读

We consider variable selection in the single-index model. We prove that the popular leave-m-out crossvalidation method has different behaviour in the single-index model from that in linear regression models or nonparametric regression models. A new consistent variable selection method, called separated crossvalidation, is proposed. Further analysis suggests that the method has better finite-sample performance and is computationally easier than leave-m-out crossvalidation.…

利用 lasso 收缩与选择回归系数及自回归阶数AI 解读

Summary The least absolute shrinkage and selection operator (‘lasso’) has been widely used in regression shrinkage and selection. We extend its application to the regression model with autoregressive errors. Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients and the other for autoregression coefficients). These tuning parameters can be easily calculated…

函数型线性回归的方法与收敛速率AI 解读

In functional linear regression, the slope “parameter” is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of contact with a range of methodologies, including statistical smoothing and deconvolution. The standard approach to estimating the slope function is based explicitly on functional principal components analysis and, consequently, on spectral…

含时变协变量的非平稳负二项时间序列模型AI 解读

Boston Harbor has a history of poor water quality, including contamination by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. Motivated by the ineffectiveness of standard Poisson mixture models and their zero-inflated counterparts, we propose a new negative binomial model for time series of Enterococcus…

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.…

自适应 Lasso 及其 Oracle 性质AI 解读

The lasso is a popular technique for simultaneous estimation and variable selection. Lasso variable selection has been shown to be consistent under certain conditions. In this work we derive a necessary condition for the lasso variable selection to be consistent. Consequently, there exist certain scenarios where the lasso is inconsistent for variable selection. We then propose a new version of the lasso, called the adaptive lasso, where adaptive weights are used for…