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高维情形下主成分得分的收敛与预测AI 解读

A number of settings arise in which it is of interest to predict Principal Component (PC) scores for new observations using data from an initial sample. In this paper, we demonstrate that naive approaches to PC score prediction can be substantially biased towards 0 in the analysis of large matrices. This phenomenon is largely related to known inconsistency results for sample eigenvalues and eigenvectors as both dimensions of the matrix increase. For the spiked eigenvalue…

非多项式维数广义线性模型中的确定独立筛选AI 解读

Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849–911] propose an independent screening framework by ranking the marginal correlations. They showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with Gaussian covariates and…

函数型线性回归的再生核希尔伯特空间方法AI 解读

We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive definite kernels, we obtain shaper results on the minimax rates of convergence and show that smoothness regularized estimators achieve the optimal rates of convergence for both prediction and estimation under conditions weaker than those…

惩罚化高维经验似然AI 解读

We propose penalized empirical likelihood for parameter estimation and variable selection for problems with diverging numbers of parameters. Our results are demonstrated for estimating the mean vector in multivariate analysis and regression coefficients in linear models. By using an appropriate penalty function, we showthat penalized empirical likelihood has the oracle property. That is, with probability tending to 1, penalized empirical likelihood identifies the true model…

Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure. Very recently, the first results concerning kernel random matrices with high-dimensional input data were obtained, in a setting where the data was sampled from a genuinely high-dimensional structure—similar to standard assumptions in…

函数型与高维数据有效降维空间的维数判定AI 解读

In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these projections is called the effective dimension reduction (EDR) space. To determine the dimensionality of the EDR space, we focus on the leading principal component scores of the predictor, and propose two sequential χ2 testing procedures under the…

Hawkes过程的自适应估计及其基因组分析应用AI 解读

The aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along DNA sequences. These events are modeled by a Hawkes process. The biological problem is actually complex enough to need a nonasymptotic penalized model selection approach. We provide a theoretical penalty that satisfies an oracle inequality even for quite complex families of models. The consecutive theoretical estimator is shown to be adaptive…

高维线性模型中的通用预言机不等式AI 解读

This paper deals with recovering an unknown vector θ from the noisy data Y = Aθ + σξ, where A is a known (m × n)-matrix and ξ is a white Gaussian noise. It is assumed that n is large and A may be severely ill-posed. Therefore, in order to estimate θ, a spectral regularization method is used, and our goal is to choose its regularization parameter with the help of the data Y. For spectral regularization methods related to the so-called ordered smoothers [see Kneip Ann.…

微阵列数据中基因方差的非参数估计AI 解读

Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman-Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is…

矩阵不确定性下的稀疏恢复AI 解读

We consider the model y = Xθ∗ + ξ, Z = X + Ξ, where the random vector y ∈ ℝn and the random n × p matrix Z are observed, the n × p matrix X is unknown, Ξ is an n × p random noise matrix, ξ ∈ ℝn is a noise independent of Ξ, and θ∗ is a vector of unknown parameters to be estimated. The matrix uncertainty is in the fact that X is observed with additive error. For dimensions p that can be much larger than the sample size n, we consider the estimation of sparse vectors θ∗. Under…

变量选择中贝叶斯与经验贝叶斯的多重性调整AI 解读

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham’s-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable…

通过求解逆问题进行非参数估计：以变换模型为例AI 解读

This paper considers a semi‐parametric version of the transformation model φ (Y) =β′X+U under exogeneity or instrumental variables assumptions (E(U∣X) = 0 or . This model is used as an example to illustrate the practice of the estimation by solving linear functional equations. This paper is specially focused on the data‐driven selection of the regularization parameter and of the bandwidths. Simulations experiments illustrate the relevance of this approach.

带变量选择的时间序列二元选择风险最小化AI 解读

This paper considers the problem of predicting binary choices by selecting from a possibly large set of candidate explanatory variables, which can include both exogenous variables and lagged dependent variables. We consider risk minimization with the risk function being the predictive classification error. We study the convergence rates of empirical risk minimization in both the frequentist and Bayesian approaches. The Bayesian treatment uses a Gibbs posterior constructed…

基于 Boosting 与径向基神经网络近似的鞅差假设检验AI 解读

The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function (RBF) neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a, 2003b). However, unlike that work we provide a formal theoretical justification for the validity of these tests and present some new general…

部分线性模型的方差分析与 F 检验：环境健康数据应用AI 解读

Fish consumption during pregnancy exposes the fetus to both the neurotoxicant methylmercury and nutrients known to be beneficial for brain development. When nutrient status is not measured, maternal methylmercury levels may be a partial biomarker for both toxic and nutrient exposures. It is therefore necessary to employ a flexible model—such as the partial linear model—that will allow for possible nonlinear trends of methylmercury. To enhance interpretations of fitting a…

结构化高维协变量空间中的贝叶斯变量选择及基因组学应用AI 解读

We consider the problem of variable selection in regression modeling in high-dimensional spaces where there is known structure among the covariates. This is an unconventional variable selection problem for two reasons: (1) The dimension of the covariate space is comparable, and often much larger, than the number of subjects in the study, and (2) the covariate space is highly structured, and in some cases it is desirable to incorporate this structural information in to the…

稀疏高维有向无环图估计的惩罚似然方法AI 解读

Directed acyclic graphs are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical and biological systems where directed edges between nodes represent the influence of components of the system on each other. Estimation of directed graphs from observational data is computationally NP-hard. In addition, directed graphs with the same structure may be indistinguishable based on…

单调回归的分组 Brunk 估计与惩罚样条估计AI 解读

We study a class of monotone univariate regression estimators. We use B-splines to approximate an underlying regression function and estimate spline coefficients based on grouped data. We investigate asymptotic properties of two monotone estimators: a grouped Brunk estimator and a penalized monotone estimator. These estimators are consistent at the boundary and their mean square errors achieve optimal convergence rates under suitable assumptions of the true regression…

高维协方差矩阵 Cholesky 正则化的新方法AI 解读

In this paper we propose a new regression interpretation of the Cholesky factor of the covariance matrix, as opposed to the well-known regression interpretation of the Cholesky factor of the inverse covariance, which leads to a new class of regularized covariance estimators suitable for high-dimensional problems. Regularizing the Cholesky factor of the covariance via this regression interpretation always results in a positive definite estimator. In particular, one can obtain…

用于高维回归与分类的惩罚 Bregman 散度AI 解读

Regularization methods are characterized by loss functions measuring data fits and penalty terms constraining model parameters. The commonly used quadratic loss is not suitable for classification with binary responses, whereas the loglikelihood function is not readily applicable to models where the exact distribution of observations is unknown or not fully specified. We introduce the penalized Bregman divergence by replacing the negative loglikelihood in the conventional…

SPADES 稀疏密度估计与混合模型AI 解读

This paper studies sparse density estimation via ℓ1 penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a general sparsity oracle inequality that the SPADES estimates satisfy. We offer a…

非参数可加模型中的变量选择AI 解读

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component…

半参数相对风险Cox模型的惩罚变量选择AI 解读

We study the Cox models with semiparametric relative risk, which can be partially linear with one nonparametric component, or multiple additive or nonadditive nonparametric components. A penalized partial likelihood procedure is proposed to simultaneously estimate the parameters and select variables for both the parametric and the nonparametric parts. Two penalties are applied sequentially. The first penalty, governing the smoothness of the multivariate nonlinear covariate…

组稀疏性的益处AI 解读

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.