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基于似然的变量选择与精确参数估计AI 解读

In high-dimensional data analysis, feature selection becomes one means for dimension reduction, which proceeds with parameter estimation. Concerning accuracy of selection and estimation, we study nonconvex constrained and regularized likelihoods in the presence of nuisance parameters. Theoretically, we show that constrained L(0)-likelihood and its computational surrogate are optimal in that they achieve feature selection consistency and sharp parameter estimation, under one…

依赖高维数据的跨维度推断AI 解读

A growing number of modern scientific problems in areas such as genomics, neurobiology, and spatial epidemiology involve the measurement and analysis of thousands of related features that may be stochastically dependent at arbitrarily strong levels. In this work, we consider the scenario where the features follow a multivariate Normal distribution. We demonstrate that dependence is manifested as random variation shared among features, and that standard methods may yield…

条件图模型的稀疏估计及其基因网络应用AI 解读

In many applications the graph structure in a network arises from two sources: intrinsic connections and connections due to external effects. We introduce a sparse estimation procedure for graphical models that is capable of isolating the intrinsic connections by removing the external effects. Technically, this is formulated as a conditional graphical model, in which the external effects are modeled as predictors, and the graph is determined by the conditional precision…

由支持函数估计凸集的最优收敛率AI 解读

We present a minimax optimal solution to the problem of estimating a compact, convex set from finitely many noisy measurements of its support function. The solution is based on appropriate regularizations of the least squares estimator. Both fixed and random designs are considered.

UPS 实现高维变量选择的最优相图AI 解读

Consider a linear model Y = Xβ + z, z ∼ N(0, In). Here, X = Xn,p, where both p and n are large, but p > n. We model the rows of X as i.i.d. samples from N(0, 1/n Ω), where Ω is a p × p correlation matrix, which is unknown to us but is presumably sparse. The vector β is also unknown but has relatively few nonzero coordinates, and we are interested in identifying these nonzeros. We propose the Univariate Penalization Screeing (UPS) for variable selection. This is a screen and…

超高维回归中基于重拟合交叉验证的方差估计AI 解读

Summary Variance estimation is a fundamental problem in statistical modelling. In ultrahigh dimensional linear regression where the dimensionality is much larger than the sample size, traditional variance estimation techniques are not applicable. Recent advances in variable selection in ultrahigh dimensional linear regression make this problem accessible. One of the major problems in ultrahigh dimensional regression is the high spurious correlation between the unobserved…

非零阈值 Tobit 模型中的聚焦信息准则、模型选择与模型平均AI 解读

Claeskens and Hjort (2003) have developed a focused information criterion (FIC) for model selection that selects different models based on different focused functions with those functions tailored to the parameters singled out for interest. Hjort and Claeskens (2003) also have presented model averaging as an alternative to model selection, and suggested a local misspecification framework for studying the limiting distributions and asymptotic risk properties of post-model…

最优工具变量的稀疏模型与方法：征收权应用AI 解读

We develop results for the use of LASSO and Post-LASSO methods to form firststage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n.We rigorously develop asymptotic distribution and inference theory for the resulting IV estimators and provide conditions under which these estimators are asymptotically oracle-efficient.In simulation experiments, the…

结构分位数效应的非参数工具变量估计AI 解读

We study the asymptotic distribution of Tikhonov Regularized estimation of quantile structural effects implied by a nonseparable model. The nonparametric instrumental variable estimator is based on a minimum distance principle. We show that the minimum distance problem without regularization is locally ill-posed, and consider penalization by the norms of the parameter and its derivatives. We derive pointwise asymptotic normality and develop a consistent estimator of the…

广义残差可能不光滑的非参数条件矩模型估计AI 解读

This paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables. This is a nonparametric nonlinear instrumental variables (IV) problem. We propose a class of penalized sieve minimum distance (PSMD) estimators, which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the…

平方根 lasso：通过锥规划实现枢轴式稀疏信号恢复AI 解读

We propose a pivotal method for estimating high-dimensional sparse linear regression models, where the overall number of regressors p is large, possibly much larger than n, but only s regressors are significant. The method is a modification of the lasso, called the square-root lasso. The method is pivotal in that it neither relies on the knowledge of the standard deviation σ nor does it need to pre-estimate σ. Moreover, the method does not rely on normality or…

协方差矩阵的稀疏估计AI 解读

We suggest a method for estimating a covariance matrix on the basis of a sample of vectors drawn from a multivariate normal distribution. In particular, we penalize the likelihood with a lasso penalty on the entries of the covariance matrix. This penalty plays two important roles: it reduces the effective number of parameters, which is important even when the dimension of the vectors is smaller than the sample size since the number of parameters grows quadratically in the…

变异函数及其谱的非参数估计AI 解读

In the study of intrinsically stationary spatial processes, a new nonparametric variogram estimator is proposed through its spectral representation. The methodology is based on estimation of the variogram’s spectrum by solving a regularized inverse problem through quadratic programming. The estimated variogram is guaranteed to be conditionally negative-definite. Simulation shows that our estimator is flexible and generally has smaller mean integrated squared error than the…

近似因子模型中的高维协方差矩阵估计AI 解读

The variance covariance matrix plays a central role in the inferential theories of high dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By…

非多项式维度下 Cox 比例风险模型的正则化AI 解读

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of non-concave penalized methods for non-polynomial (NP) dimensional data with censoring in the framework of Cox's proportional hazards model. A class of folded-concave penalties are employed and both LASSO and…

非参数条件矩限制模型的后验一致性AI 解读

This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g0. We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior…

冯·诺依曼熵惩罚与低秩矩阵估计AI 解读

We study a problem of estimation of a Hermitian nonnegatively definite matrix ρ of unit trace (e.g., a density matrix of a quantum system) based on n i.i.d. measurements (X1, Y1), …, (Xn, Yn), where Yj = tr(ρXj) + ξj, j = 1, …, n, {Xj} being random i.i.d. Hermitian matrices and {ξj} being i.i.d. random variables with ${\mathbb{E}}(\xi_{j}|X_{j})=0$. The estimator $$\hat{\rho}^{\varepsilon }:=\mathop{\arg\min}_{S\in{\mathcal{S}}}\Biggl[n^{-1}\sum_{j=1}^{n}\bigl(Y_{j}-\operatorname{tr}(SX_{j})\bigr)^{2}+\varepsilon \operatorname{tr}(S\log S)\Biggr] $$…

一般高斯图模型的贝叶斯推断及其在多变量格点数据中的应用AI 解读

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated with graphs that can be decomposable or non-decomposable. We extend our sampling algorithms to a novel class of conditionally autoregressive models for sparse estimation in multivariate lattice data, with a special emphasis on the analysis…

用于蛋白质组通路分析的正则化 Hotelling T² 检验AI 解读

Recent proteomic studies have identified proteins related to specific phenotypes. In addition to marginal association analysis for individual proteins, analyzing pathways (functionally related sets of proteins) may yield additional valuable insights. Identifying pathways that differ between phenotypes can be conceptualized as a multivariate hypothesis testing problem: whether the mean vector μ of a p-dimensional random vector X is μ0. Proteins within the same biological…

用于局地校准概率定量降水预测的地统计模型平均AI 解读

Accurate weather benefit many key societal functions and activities, including agriculture, transportation, recreation, and basic human and infrastructural safety. Over the past two decades, ensembles of numerical weather prediction models have been developed, in which multiple estimates of the current state of the atmosphere are used to generate probabilistic forecasts for future weather events. However, ensemble systems are uncalibrated and biased, and thus need to be…

离散指数族的不稳定性、敏感性与退化AI 解读

In applications to dependent data, first and foremost relational data, a number of discrete exponential family models has turned out to be near-degenerate and problematic in terms of Markov chain Monte Carlo simulation and statistical inference. We introduce the notion of instability with an eye to characterize, detect, and penalize discrete exponential family models that are near-degenerate and problematic in terms of Markov chain Monte Carlo simulation and statistical…

采用正交象限正态先验的弹性网回归建模AI 解读

The elastic net procedure is a form of regularized optimization for linear regression that provides a bridge between ridge regression and the lasso. The estimate that it produces can be viewed as a Bayesian posterior mode under a prior distribution implied by the form of the elastic net penalty. This article broadens the scope of the Bayesian connection by providing a complete characterization of a class of prior distributions that generate the elastic net estimate as the…

正则化回归估计推断的扰动方法AI 解读

Analysis of high dimensional data often seeks to identify a subset of important features and assess their effects on the outcome. Traditional statistical inference procedures based on standard regression methods often fail in the presence of high-dimensional features. In recent years, regularization methods have emerged as promising tools for analyzing high dimensional data. These methods simultaneously select important features and provide stable estimation of their…

结合混合效应建模的高维常微分方程动态基因调控网络识别AI 解读

Gene regulation is a complicated process. The interaction of many genes and their products forms an intricate biological network. Identification of this dynamic network will help us understand the biological process in a systematic way. However, the construction of such a dynamic network is very challenging for a high-dimensional system. In this article we propose to use a set of ordinary differential equations (ODE), coupled with dimensional reduction by clustering and…