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交互固定效应动态面板模型的收缩估计AI 解读

We consider the problem of determining the number of factors and selecting the proper regressors in linear dynamic panel data models with interactive fixed effects. Based on the preliminary estimates of the slope parameters and factors a la Bai (2009) and Moon and Weidner (2015), we propose a method for simultaneous selection of regressors and factors and estimation through the method of adaptive group Lasso (least absolute shrinkage and selection operator). We show that…

面板数据中潜在分组结构的识别AI 解读

This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized techniques. We consider both linear and nonlinear models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown. Two approaches are considered—penalized profile likelihood (PPL) estimation for the general nonlinear models without endogenous regressors, and penalized GMM (PGMM)…

超高维广义半变系数模型的模型选择与结构识别AI 解读

In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO…

门限自回归模型的 LASSO 估计AI 解读

This paper develops a novel approach for estimating a threshold autoregressive (TAR) model with multiple-regimes and establishes its large sample properties. By reframing the problem in a regression variable selection context, a least absolute shrinkage and selection operator (LASSO) procedure is proposed to estimate a TAR model with an unknown number of thresholds, where the computation can be performed efficiently. It is further shown that the number and the location of…

时间序列与金融计量经济学前沿：概览AI 解读

Two of the fastest growing frontiers in econometrics and quantitative finance are time series and financial econometrics. Significant theoretical contributions to financial econometrics have been made by experts in statistics, econometrics, mathematics, and time series analysis. The purpose of this special issue of the journal on “Frontiers in Time Series and Financial Econometrics” is to highlight several areas of research by leading academics in which novel methods have…

具有变量选择的函数型指数系数模型AI 解读

We consider model (variable) selection in a semi-parametric time series model with functional coefficients. Variable selection in the semi-parametric model must account for the fact that the parametric part of the model is estimated at a faster convergence rate than the nonparametric component. Our variable selection procedures employ a smoothly clipped absolute deviation penalty function and consist of two steps. The first is to select covariates with functional…

Lasso 估计量的成对 Bootstrap 有效性AI 解读

We study the validity of the pairs bootstrap for lasso estimators in linear regression models with random covariates and heteroscedastic error terms. We show that the naive pairs bootstrap does not provide a valid method for approximating the distribution of the lasso estimator. To overcome this deficiency, we introduce a modified pairs bootstrap procedure and prove its consistency. Finally, we consider the adaptive lasso and show that the modified pairs bootstrap…

超高维回归的拆分合并贝叶斯变量选择方法AI 解读

Summary We propose a Bayesian variable selection approach for ultrahigh dimensional linear regression based on the strategy of split and merge. The approach proposed consists of two stages: split the ultrahigh dimensional data set into a number of lower dimensional subsets and select relevant variables from each of the subsets, and aggregate the variables selected from each subset and then select relevant variables from the aggregated data set. Since the approach proposed…

协变量可能多于观测时平均处理效应的稳健推断AI 解读

This paper concerns robust inference on average treatment effects following model selection. Under selection on observables, we construct confidence intervals using a doubly-robust estimator that are robust to model selection errors and prove their uniform validity over a large class of models that allows for multivalued treatments with heterogeneous effects and selection amongst (possibly) more covariates than observations. The semiparametric efficiency bound is attained…

识别表达数量性状位点的贝叶斯划分模型AI 解读

Expression quantitative trait loci (eQTLs) are genomic locations associated with changes of expression levels of certain genes. By assaying gene expressions and genetic variations simultaneously on a genome-wide scale, scientists wish to discover genomic loci responsible for expression variations of a set of genes. The task can be viewed as a multivariate regression problem with variable selection on both responses (gene expression) and covariates (genetic variations),…

基于倒数 L1 正则化的高维变量选择AI 解读

During the past decade, penalized likelihood methods have been widely used in variable selection problems, where the penalty functions are typically symmetric about 0, continuous and nondecreasing in (0, ∞). We propose a new penalized likelihood method, reciprocal Lasso (or in short, rLasso), based on a new class of penalty functions that are decreasing in (0, ∞), discontinuous at 0, and converge to infinity when the coefficients approach zero. The new penalty functions give…

贝叶斯压缩回归AI 解读

As an alternative to variable selection or shrinkage in high-dimensional regression, we propose to randomly compress the predictors prior to analysis. This dramatically reduces storage and computational bottlenecks, performing well when the predictors can be projected to a low-dimensional linear subspace with minimal loss of information about the response. As opposed to existing Bayesian dimensionality reduction approaches, the exact posterior distribution conditional on the…

用于最优收缩的 Dirichlet–Laplace 先验AI 解读

regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimensions. This has motivated continuous shrinkage priors, which can be expressed as global-local scale mixtures of Gaussians,…

超高维数据的全局自适应分位数回归AI 解读

Quantile regression has become a valuable tool to analyze heterogeneous covaraite-response associations that are often encountered in practice. The development of quantile regression methodology for high-dimensional covariates primarily focuses on the examination of model sparsity at a single or multiple quantile levels, which are typically prespecified ad hoc by the users. The resulting models may be sensitive to the specific choices of the quantile levels, leading to…

函数型加性回归AI 解读

We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar response, $Y$, in two key respects. First, FAR uses a penalized least squares optimization approach to efficiently deal with high-dimensional problems involving a large number of functional predictors. Second, FAR extends beyond the…

高维协变量非线性交互的广义加性系数模型估计与推断AI 解读

In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423–1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this paper, we propose estimation and inference procedures for the GACM when the dimension of the variables is high. Specifically, we propose a groupwise penalization based procedure to distinguish significant covariates for the…

采用稀疏先验的贝叶斯线性回归AI 解读

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients…

多样本对齐稀疏信号的最优检测AI 解读

We describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk–Jones and the higher-criticism test statistics evaluated over pooled scans, and an average likelihood ratio over the critical boundary. We show in our results an inter-play between the scale of the sequence length to signal length ratio, and the…

通过 Knockoff 变量控制错误发现率AI 解读

In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)—the expected fraction of false discoveries among all discoveries—is not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper…

具有收敛保证的高维偏相关估计凸伪似然框架AI 解读

Summary Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l 1-penalties to either parametric likelihoods, or regularized regression/pseudolikelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudolikelihood-based objective functions have provable convergence guarantees, it is not clear…

部分观测函数型数据的主成分分析与补全AI 解读

Summary Functional data are traditionally assumed to be observed on the same domain. Motivated by a data set of heart rate temporal profiles, we develop methodology for the analysis of incomplete functional samples where each curve may be observed on a subset of the domain and unobserved elsewhere. We formalize this observation regime and develop the fundamental procedures of functional data analysis for this framework: estimation of parameters (mean and covariance operator)…

异质大规模数据中的最大最小效应AI 解读

Large-scale data are often characterized by some degree of inhomogeneity as data are either recorded in different time regimes or taken from multiple sources. We look at regression models and the effect of randomly changing coefficients, where the change is either smoothly in time or some other dimension or even without any such structure. Fitting varying-coefficient models or mixture models can be appropriate solutions but are computationally very demanding and often return…

广义函数型线性模型的非参数推断AI 解读

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for regression mean, prediction intervals for future response and various statistical procedures for hypothesis testing. In particular, one procedure for testing global behaviors of the slope function is adaptive to the smoothness of the slope function…

稀疏高维时间序列模型中的正则化估计AI 解读

Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically distributed (i.i.d.) samples. In this work, we focus on stable Gaussian processes and investigate the theoretical properties of $\ell_{1}$-regularized estimates in two important statistical problems in the context of high-dimensional time series:…