论文检索

高维稀疏环境中的两样本协方差矩阵检验与支持集恢复AI 解读

In the high-dimensional setting, this article considers three interrelated problems: (a) testing the equality of two covariance matrices and ; (b) recovering the support of ; and (c) testing the equality of and row by row. We propose a new test for testing the hypothesis H 0: and investigate its theoretical and numerical properties. The limiting null distribution of the test statistic is derived and the power of the test is studied. The test is shown to enjoy certain…

实验干预下稀疏因果高斯网络的学习：正则化与坐标下降AI 解读

Causal networks are graphically represented by directed acyclic graphs (DAGs). Learning causal networks from data is a challenging problem due to the size of the space of DAGs, the acyclicity constraint placed on the graphical structures, and the presence of equivalence classes. In this article, we develop an L 1-penalized likelihood approach to estimate the structure of causal Gaussian networks. A blockwise coordinate descent algorithm, which takes advantage of the…

高维稀疏加性风险回归AI 解读

High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of regularization methods for simultaneous variable selection and estimation in the additive hazards model, by combining the nonconcave penalized likelihood approach and the pseudoscore method. In a high-dimensional setting where the…

大模型空间中贝叶斯变量选择的采样策略AI 解读

One important aspect of Bayesian model selection is how to deal with huge model spaces, since the exhaustive enumeration of all the models entertained is not feasible and inferences have to be based on the very small proportion of models visited. This is the case for the variable selection problem with a moderately large number of possible explanatory variables considered in this article. We review some of the strategies proposed in the literature, from a theoretical point…

高维经济数据插补：农业资源管理调查应用AI 解读

In this article, we consider imputation in the USDA’s Agricultural Resource Management Survey (ARMS) data, which is a complex, high-dimensional economic dataset. We develop a robust joint model for ARMS data, which requires that variables are transformed using a suitable class of marginal densities (e.g., skew normal family). We assume that the transformed variables may be linked through a Gaussian copula, which enables construction of the joint model via a sequence of…

利用贝叶斯变量选择进行VAR预测AI 解读

SUMMARY This paper develops methods for automatic selection of variables in Bayesian vector autoregressions (VARs) using the Gibbs sampler. In particular, I provide computationally efficient algorithms for stochastic variable selection in generic linear and nonlinear models, as well as models of large dimensions. The performance of the proposed variable selection method is assessed in forecasting three major macroeconomic time series of the UK economy. Data‐based…

通过导数约束建模内生解释变量与异质性结构方程AI 解读

In this paper, I present a general modeling framework for nonparametric models with endogenous regressors and heterogeneity. I show that many existing models in the literature can be derived from a structural equation with unobserved heterogeneity by imposing constancy assumptions on the first and second derivatives. I consider a less restrictive model that imposes constancy assumptions on the second partial derivative of the structural equation. Assuming the existence of…

高维异质数据的分位数自适应无模型变量筛选AI 解读

We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus making it more flexible to accommodate heterogeneity; (2) it is model-free and avoids the difficult task of specifying the form of a statistical model in a high dimensional space. Our nonlinear independence screening procedure employs spline…

非参数回归中的空间自适应采样AI 解读

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function…

随机效应与固定效应面板模型中的神谕有效变量选择AI 解读

This paper generalizes the results for the Bridge estimator of Huang, Horowitz, and Ma (2008) to linear random and fixed effects panel data models which are allowed to grow in both dimensions. In particular, we show that the Bridge estimator isoracle efficient. It can correctly distinguish between relevant and irrelevant variables and the asymptotic distribution of the estimators of the coefficients of the relevant variables is the same as if only these had been included in…

空间广义线性混合模型的降维与空间混杂缓解AI 解读

Summary Non-Gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for dependence to ensure reliable inference for the regression coefficients. The spatial generalized linear mixed model offers a very popular and flexible approach to modelling such data, but this model suffers from two major shortcomings:…

针对缺失值与观察性研究进行处理前变量调整的Mann–Whitney检验AI 解读

Summary The conventional Wilcoxon or Mann–Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pretreatment variables. We propose an approach to adjust the Mann–Whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the…

带错误控制的变量选择：再论稳定性选择AI 解读

Summary Stability selection was recently introduced by Meinshausen and Bühlmann as a very general technique designed to improve the performance of a variable selection algorithm. It is based on aggregating the results of applying a selection procedure to subsamples of the data. We introduce a variant, called complementary pairs stability selection, and derive bounds both on the expected number of variables included by complementary pairs stability selection that have low…

向量误差修正模型中的随机搜索变量选择及英国宏观应用AI 解读

SUMMARY This paper develops methods for stochastic search variable selection (currently popular with regression and vector autoregressive models) for vector error correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK…

误设模型中贝叶斯推断的风险与三明治协方差矩阵AI 解读

It is well known that, in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo-true value and has an asymptotically normal sampling distribution with “sandwich” covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal, and of asymptotic variance that is, in general, different than the sandwich matrix. It is shown that due to this discrepancy, Bayesian inference about the pseudo-true parameter value is,…

随机搜索变量选择中的有限总体估计量AI 解读

Monte Carlo algorithms are commonly used to identify a set of models for Bayesian model selection or model averaging. Because empirical frequencies of models are often zero or one in high-dimensional problems, posterior probabilities calculated from the observed marginal likelihoods, renormalized over the sampled models, are often employed. Such estimates are the only recourse in several newer stochastic search algorithms. In this paper, we prove that renormalization of…

尺度化稀疏线性回归AI 解读

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual square and scaling the penalty in proportion to the estimated noise level. The iterative algorithm costs little beyond the computation of a path or grid of the sparse regression estimator for penalty levels above a proper threshold. For the…

离散度算子与抗异常的二阶函数型数据分析AI 解读

Inferences related to the second-order properties of functional data, as expressed by covariance structure, can become unreliable when the data are non-Gaussian or contain unusual observations. In the functional setting, it is often difficult to identify atypical observations, as their distinguishing characteristics can be manifold but subtle. In this paper, we introduce the notion of a dispersion operator, investigate its use in probing the second-order structure of…

惩罚平衡抽样AI 解读

Linear mixed models cover a wide range of statistical methods, which have found many uses in the estimation for complex surveys. The purpose of this work is to consider methods by which linear mixed models may be used at the design stage of a survey to incorporate available auxiliary information. This paper reviews the ideas of balanced sampling and the cube algorithm, and proposes an implementation of the latter by which penalized balanced samples can be selected. Such…

块稀疏信号 ℓ₁ 恢复的精度保证AI 解读

We introduce a general framework to handle structured models (sparse and block-sparse with possibly overlapping blocks). We discuss new methods for their recovery from incomplete observation, corrupted with deterministic and stochastic noise, using block-$\ell_{1}$ regularization. While the current theory provides promising bounds for the recovery errors under a number of different, yet mostly hard to verify conditions, our emphasis is on verifiable conditions on the problem…

留受试者交叉验证的渐近最优性与高效计算AI 解读

Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving the associated optimization problem is computationally expensive, especially when there are multiple tuning parameters. In this paper, by focusing on the penalized spline method, we show that the leave-subject-out CV is optimal in the sense…

自适应函数型线性回归AI 解读

We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395–408] have shown that a thresholded projection estimator can attain up to a constant minimax-rates of convergence in a general framework which allows us to cover the prediction problem with respect to the mean squared prediction error as well as the estimation of the…

广义平滑有限混合模型AI 解读

We propose a general class of models and a unified Bayesian inference methodology for flexibly estimating the density of a response variable conditional on a possibly high-dimensional set of covariates. Our model is a finite mixture of component models with covariate-dependent mixing weights. The component densities can belong to any parametric family, with each model parameter being a deterministic function of covariates through a link function. Our MCMC methodology allows…

跨国增长回归中的变量选择与函数形式不确定性AI 解读

Regression analyses of cross-country economic growth data are complicated by two main forms of model uncertainty: the uncertainty in selecting explanatory variables and the uncertainty in specifying the functional form of the regression function. Most discussions in the literature address these problems independently, yet a joint treatment is essential. We present a new framework that makes such a joint treatment possible, using flexible nonlinear models specified by…