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讨论：变量数远大于样本量时的 Dantzig 选择器统计估计AI 解读

Professors Candès and Tao are to be congratulated for their innovative and valuable contribution to high-dimensional sparse recovery and model selection.The analysis of vast data sets now commonly arising in scientific investigations poses many statistical challenges not present in smaller scale studies.Many of these data sets exhibit sparsity where most of the data corresponds to noise and only a small fraction is of interest.The needs of this research have excited much…

未知连接函数的一般非参数回归模型的速率最优估计AI 解读

This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that…

稀疏正态混合模型的估计与置信集AI 解读

For high dimensional statistical models, researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients. Such situations lead to some very subtle statistical problems. In particular, Ingster and Donoho and Jin have considered a sparse normal means testing problem, in which they described the precise demarcation or detection boundary. Meinshausen and Rice have shown that it is even possible to estimate consistently…

讨论：Lasso、L2Boosting 与 Dantzig 三种相关方法AI 解读

We would like to congratulate the authors for their thought-provoking and interesting paper.The Dantzig paper is on the timely topic of high-dimensional data modeling that has been the center of much research lately and where many exciting results have been obtained.It also falls in the very hot area at the interface of statistics and optimization: ℓ 1 -constrained minimization in linear models for computationally efficient model selection, or sparse model estimation (Chen,…

Dantzig 选择器：变量数远大于样本量时的统计估计AI 解读

In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y=Xβ+z, where β∈Rp is a parameter vector of interest, X is a data matrix with possibly far fewer rows than columns, n≪p, and the zi’s are i.i.d. N(0, σ2). Is it possible to estimate β reliably based on the noisy data y? To estimate β, we introduce a new estimator—we call it the Dantzig selector—which is a…

摘要暂缺

协变量随机缺失回归模型的筛极大似然估计AI 解读

Missing covariates are common in regression problems. We propose a new semiparametric method based on a fully nonparametric distribution for the missing covariates that are assumed to be missing at random. The method of sieve maximum likelihood estimation is used to obtain the estimators of the regression coefficients. These estimators are shown to be consistent and asymptotically normal with their asymptotic covariance matrix that achieves the semiparametric efficiency…

相关误差下惩罚样条平滑的一则说明AI 解读

We investigate the behavior of data-driven smoothing parameters for penalized spline regression in the presence of correlated data. It has been shown for other smoothing methods that mean squared error minimizers, such as (generalized) cross-validation or the Akaike information criterion, are extremely sensitive to misspecifications of the correlation structure resulting in over- or (under-)fitting the data. In contrast to this, we show that a maximum likelihood–based choice…

正态均值问题中贝叶斯检验与估计结合方法的最优性AI 解读

We consider a problem of recovering a high-dimensional vector μ observed in white noise, where the unknown vector μ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of l0-type penalties. The penalties are associated with various choices of the prior distributions πn(⋅) on the number of nonzero entries of μ and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule…

自旋玻璃中的估计：第一步AI 解读

The Sherrington–Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under bare minimal conditions, we establish the $\sqrt{N}$-consistency of the maximum pseudolikelihood estimate of the natural parameter in this family, even at critical temperatures. Since very little is known about the low and critical…

基于 φ 散度的拟合优度检验AI 解读

A unified family of goodness-of-fit tests based on φ-divergences is introduced and studied. The new family of test statistics Sn(s) includes both the supremum version of the Anderson–Darling statistic and the test statistic of Berk and Jones [Z. Wahrsch. Verw. Gebiete 47 (1979) 47–59] as special cases (s=2 and s=1, resp.). We also introduce integral versions of the new statistics. We show that the asymptotic null distribution theory of Berk and Jones [Z. Wahrsch. Verw.…

Lasso 的有效自由度AI 解读

We study the effective degrees of freedom of the lasso in the framework of Stein’s unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degrees of freedom of the lasso—a conclusion that requires no special assumption on the predictors. In addition, the unbiased estimator is shown to be asymptotically consistent. With these results on hand, various model selection criteria—Cp, AIC and BIC—are available, which, along…

长记忆模型中遗漏非线性的检验AI 解读

This article constructs tests for the presence of nonlinearity of unknown form in addition to a fractionally integrated, long-memory component in a time series process. The tests are based on artificial neural network approximations and do not restrict the parametric form of the nonlinearity. Some theoretical results for the new tests are obtained, and detailed simulation evidence on the power of the tests is presented. The new methodology is then applied to a wide variety…

贝叶斯非参数混合模型中强化机制的控制AI 解读

Summary The paper deals with the problem of determining the number of components in a mixture model. We take a Bayesian non-parametric approach and adopt a hierarchical model with a suitable non-parametric prior for the latent structure. A commonly used model for such a problem is the mixture of Dirichlet process model. Here, we replace the Dirichlet process with a more general non-parametric prior obtained from a generalized gamma process. The basic feature of this model is…

广义线性模型的 L1 正则化路径算法AI 解读

Summary We introduce a path following algorithm for L1-regularized generalized linear models. The L1-regularization procedure is useful especially because it, in effect, selects variables according to the amount of penalization on the L1-norm of the coefficients, in a manner that is less greedy than forward selection–backward deletion. The generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the…

函数型主成分回归与函数型偏最小二乘AI 解读

Regression of a scalar response on signal predictors, such as near-infrared (NIR) spectra of chemical samples, presents a major challenge when, as is typically the case, the dimension of the signals far exceeds their number. Most solutions to this problem reduce the dimension of the predictors either by regressing on components [e.g., principal component regression (PCR) and partial least squares (PLS)] or by smoothing methods, which restrict the coefficient function to the…

有限混合回归模型中的变量选择AI 解读

In the applications of finite mixture of regression (FMR) models, often many covariates are used, and their contributions to the response variable vary from one component to another of the mixture model. This creates a complex variable selection problem. Existing methods, such as the Akaike information criterion and the Bayes information criterion, are computationally expensive as the number of covariates and components in the mixture model increases. In this article we…

通过最小二乘近似统一 LASSO 估计AI 解读

We propose a method of least squares approximation (LSA) for unified yet simple LASSO estimation. Our general theoretical framework includes ordinary least squares, generalized linear models, quantile regression, and many others as special cases. Specifically, LSA can transfer many different types of LASSO objective functions into their asymptotically equivalent least squares problems. Thereafter, the standard asymptotic theory can be established and the LARS algorithm can…

最优地统计模型选择AI 解读

In many fields of science, predicting variables of interest over a study region based on noisy data observed at some locations is an important problem. Two popular methods for the problem are kriging and smoothing splines. The former assumes that the underlying process is stochastic, whereas the latter assumes it is purely deterministic. Kriging performs better than smoothing splines in some situations, but is outperformed by smoothing splines in others. However, little is…

用于发现基因调控网络的回归混合模型变量选择AI 解读

The profusion of genomic data through genome sequencing and gene expression microarray technology has facilitated statistical research in determining gene interactions regulating a biological process. Current methods generally consist of a two-stage procedure: clustering gene expression measurements and searching for regulatory “switches,” typically short, conserved sequence patterns (motifs) in the DNA sequence adjacent to the genes. This process often leads to misleading…

加州电力备用容量市场的效率AI 解读

Abstract We test the efficiency of the California electricity reserves market by examining systematic differences between its day‐ and hour‐ahead prices. We uncover significant day‐ahead premia, which we attribute to market design characteristics. On the demand side, the market design established a principal–agent relationship between the markets' buyers (principal) and their supervisory authority (agent). The agent had very limited incentives to shift reserve purchases to…

基于种群的可逆跳跃马尔可夫链蒙特卡洛AI 解读

In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of…

不可忽略非单调无应答下重复结果均值回归的估计AI 解读

We propose a new class of models for making inference about the mean of a vector of repeated outcomes when the outcome vector is incompletely observed in some study units and missingness is nonmonotone. Each model in our class is indexed by a set of unidentified selection-bias functions which quantify the residual association of the outcome at each occasion t and the probability that this outcome is missing after adjusting for variables observed prior to time t and for the…

SCAD 方法的调节参数选择AI 解读

The penalised least squares approach with smoothly clipped absolute deviation penalty has been consistently demonstrated to be an attractive regression shrinkage and selection method. It not only automatically and consistently selects the important variables, but also produces estimators which are as efficient as the oracle estimator. However, these attractive features depend on appropriately choosing the tuning parameter. We show that the commonly used the generalised…