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高维正态均值向量估计的非参数经验贝叶斯与复合决策方法AI 解读

We consider the classical problem of estimating a vector μ=(μ1, …, μn) based on independent observations Yi∼N(μi, 1), i=1, …, n. Suppose μi, i=1, …, n are independent realizations from a completely unknown G. We suggest an easily computed estimator μ̂, such that the ratio of its risk E(μ̂−μ)2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained. Our asymptotics is of a triangular array; that is, we allow the distribution G to…

参数维度随样本量增长时的自适应弹性网AI 解读

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property (Fan and Li, 2001; Fan and Peng, 2004) which ensures the optimal large sample performance. Furthermore, the high-dimensionality often induces the collinearity problem which should be properly handled by the ideal method. Many existing variable selection methods fail to…

Lasso 与 Dantzig selector 的统一分析AI 解读

We show that, under a sparsity scenario, the Lasso estimator and the Dantzig selector exhibit similar behavior. For both methods, we derive, in parallel, oracle inequalities for the prediction risk in the general nonparametric regression model, as well as bounds on the ℓp estimation loss for 1≤p≤2 in the linear model when the number of variables can be much larger than the sample size.

用于变量选择的组桥方法AI 解读

Abstract In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The existing methods, including the lasso and group lasso, are designed for either variable selection or group selection, but not for both. We propose a group bridge approach that is capable of simultaneous selection at both the group and within-group individual variable…

具有分组变量的层级惩罚 Cox 回归AI 解读

In many biological and other scientific applications, predictors are often naturally grouped. For example, in biological applications, assayed genes or proteins are grouped by biological roles or biological pathways. When studying the dependence of survival outcome on these grouped predictors, it is desirable to select variables at both the group level and the within-group level. In this article, we develop a new method to address the group variable selection problem in the…

带收缩调节的广义 Dantzig 选择器AI 解读

The Dantzig selector performs variable selection and model fitting in linear regression. It uses an L1 penalty to shrink the regression coefficients towards zero, in a similar fashion to the lasso. While both the lasso and Dantzig selector potentially do a good job of selecting the correct variables, they tend to overshrink the final coefficients. This results in an unfortunate trade-off. One can either select a high shrinkage tuning parameter that produces an accurate model…

高维小样本分类器的尺度调整AI 解读

Distance-based classifiers are generally considered to be effective at discriminating between populations that differ in location. Indeed, nearest-neighbour methods and the support vector machine are frequently used in very high-dimensional problems involving gene expression data, where it is believed that elevated levels of expression convey much of the information for classification. However, one problem inherent to distance-based classifiers is that scale differences can…

Copula结构分析AI 解读

Summary We extend the standard approach of correlation structure analysis for dimension reduction of high dimensional statistical data. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a model for the copula. For elliptical copulas a correlation-like structure remains, but different margins and non-existence of moments are possible. After introducing the new concept and deriving some theoretical…

高维问题中的协方差正则化回归与分类AI 解读

Summary We propose covariance-regularized regression, a family of methods for prediction in high dimensional settings that uses a shrunken estimate of the inverse covariance matrix of the features to achieve superior prediction. An estimate of the inverse covariance matrix is obtained by maximizing the log-likelihood of the data, under a multivariate normal model, subject to a penalty; it is then used to estimate coefficients for the regression of the response onto the…

金融波动率的样条建模AI 解读

Summary We propose a flexible generalized auto-regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B-splines of lagged observations and volatilities. Estimation of such a B-spline basis expansion is constructed within the likelihood framework for non-Gaussian observations. As the dimension of the B-spline basis is large, i.e. many parameters, we use…

参数数量发散时的收缩调节参数选择AI 解读

Summary Contemporary statistical research frequently deals with problems involving a diverging number of parameters. For those problems, various shrinkage methods (e.g. the lasso and smoothly clipped absolute deviation) are found to be particularly useful for variable selection. Nevertheless, the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters. With a fixed predictor dimension, Wang and co-worker have…

在线预测线性回归AI 解读

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard treatment of prediction in linear regression analysis has two drawbacks: (1) the classical prediction intervals guarantee that the probability of error is equal to the nominal significance level ɛ, but this property per se does not imply that the…

通过熵惩罚在凸包中实现稀疏恢复AI 解读

Let (X, Y) be a random couple in S×T with unknown distribution P and (X1, Y1), …, (Xn, Yn) be i.i.d. copies of (X, Y). Denote Pn the empirical distribution of (X1, Y1), …, (Xn, Yn). Let h1, …, hN: S↦[−1, 1] be a dictionary that consists of N functions. For λ∈ℝN, denote fλ:=∑j=1Nλjhj. Let ℓ: T×ℝ↦ℝ be a given loss function and suppose it is convex with respect to the second variable. Let (ℓ•f)(x, y):=ℓ(y; f(x)). Finally, let Λ⊂ℝN be the simplex of all probability distributions…

主成分限制最大似然估计量的一致性AI 解读

In this paper we consider two closely related problems: estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and eigenvectors of the covariance matrix for high-dimensional Gaussian vectors. In [A geometric approach to maximum likelihood estimation of covariance kernel from sparse irregular longitudinal data (2007)], a restricted maximum likelihood…

贝叶斯变量选择程序的一致性AI 解读

It has long been known that for the comparison of pairwise nested models, a decision based on the Bayes factor produces a consistent model selector (in the frequentist sense). Here we go beyond the usual consistency for nested pairwise models, and show that for a wide class of prior distributions, including intrinsic priors, the corresponding Bayesian procedure for variable selection in normal regression is consistent in the entire class of normal linear models. We find that…

变系数模型的收缩估计AI 解读

The varying coefficient model is a useful extension of the linear regression model. Nevertheless, how to conduct variable selection for the varying coefficient model in a computationally efficient manner is poorly understood. To solve the problem, we propose here a novel method, which combines the ideas of the local polynomial smoothing and the Least Absolute Shrinkage and Selection Operator (LASSO). The new method can do nonparametric estimation and variable selection…

计算高效的非参数重要性抽样AI 解读

The variance reduction established by importance sampling strongly depends on the choice of the importance sampling distribution. A good choice is often hard to achieve especially for high-dimensional integration problems. Nonparametric estimation of the optimal importance sampling distribution (known as “nonparametric importance sampling”) is a reasonable alternative to parametric approaches. In this article, nonparametric variants of both the self-normalized and the…

用于基因关联分析的对数线性模型AI 解读

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on…

动态 PET 数据的非参数残留函数分析：健康受试者脑部 FDG 研究AI 解读

Kinetic analysis is used to extract metabolic information from dynamic positron emission tomography (PET) uptake data. The theory of indicator dilutions, developed in the seminal work of Meier and Zierler (1954), provides a probabilistic framework for representation of PET tracer uptake data in terms of a convolution between an arterial input function and a tissue residue. The residue is a scaled survival function associated with tracer residence in the tissue. Nonparametric…

纵向二元与连续过程关联的联合模型及戒烟试验应用AI 解读

Joint models for the association of a longitudinal binary and a longitudinal continuous process are proposed for situations in which their association is of direct interest. The models are parameterized such that the dependence between the two processes is characterized by unconstrained regression coefficients. Bayesian variable selection techniques are used to parsimoniously model these coefficients. A Markov chain Monte Carlo (MCMC) sampling algorithm is developed for…

利用联合稀疏回归模型估计偏相关AI 解读

In this paper, we propose a computationally efficient approach -space(Sparse PArtial Correlation Estimation)- for selecting non-zero partial correlations under the high-dimension-low-sample-size setting. This method assumes the overall sparsity of the partial correlation matrix and employs sparse regression techniques for model fitting. We illustrate the performance of space by extensive simulation studies. It is shown that space performs well in both non-zero partial…

函数型数据的深度概念AI 解读

The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of many experiments in applied statistics. As a starting point for this robust analysis, we propose, analyze, and apply a new definition of depth for functional observations based on the graphic representation of the curves. Given a collection of functions, it establishes the “centrality” of an…

贝叶斯模型平均中先验假设的影响：增长回归应用AI 解读

Abstract We consider the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. We examine the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors and on predictive performance. We illustrate these issues in the context of…

扩散指数预测中的提升法AI 解读

Abstract In forecasting and regression analysis, it is often necessary to select predictors from a large feasible set. When the predictors have no natural ordering, an exhaustive evaluation of all possible combinations of the predictors can be computationally costly. This paper considers ‘boosting’ as a methodology of selecting the predictors in factor‐augmented autoregressions. As some of the predictors are being estimated, we propose a stopping rule for boosting to prevent…