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重复测量分析中非参数变系数模型的变量选择AI 解读

Nonparametric varying-coefficient models are commonly used for analysis of data measured repeatedly over time, including longitudinal and functional responses data. While many procedures have been developed for estimating the varying-coefficients, the problem of variable selection for such models has not been addressed. In this article, we present a regularized estimation procedure for variable selection that combines basis function approximations and the smoothly clipped…

二项回归模型中 Jeffreys 先验的性质与计算实现AI 解读

We study several theoretical properties of Jeffreys's prior for binomial regression models. We show that Jeffreys's prior is symmetric and unimodal for a class of binomial regression models. We characterize the tail behavior of Jeffreys's prior by comparing it with the multivariate t and normal distributions under the commonly used logistic, probit, and complementary log-log regression models. We also show that the prior and posterior normalizing constants under Jeffreys's…

函数型加性模型AI 解读

In commonly used functional regression models, the regression of a scalar or functional response on the functional predictor is assumed to be linear. This means that the response is a linear function of the functional principal component scores of the predictor process. We relax the linearity assumption and propose to replace it by an additive structure, leading to a more widely applicable and much more flexible framework for functional regression models. The proposed…

随机矩阵理论：SAMSI 研究计划介绍AI 解读

Craig Tracy and I became coorganizers and the program's scope was enlarged.It now included regularization issues, inference in graphical models, Bayesian multivariate analysis in such models, applications of random matrix theory particularly in electrical engineering, as well as applications of regularization and high dimensional multivariate analysis in geophysical models.The program was realized as a six-month session in 2006-2007 and featured not only the usual opening…

高斯图模型中的灵活协方差估计AI 解读

In this paper, we propose a class of Bayes estimators for the covariance matrix of graphical Gaussian models Markov with respect to a decomposable graph G. Working with the WPG family defined by Letac and Massam [Ann. Statist. 35 (2007) 1278–1323] we derive closed-form expressions for Bayes estimators under the entropy and squared-error losses. The WPG family includes the classical inverse of the hyper inverse Wishart but has many more shape parameters, thus allowing for…

主成分分析的有限样本近似：矩阵扰动方法AI 解读

Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of n observations (samples), each with p variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation between the eigenvalues and eigenvectors of PCA computed on a finite sample of size n, and those of the limiting population PCA as n→∞. As in machine learning, we present a finite sample theorem which holds with high probability for the closeness…

大型Wishart矩阵的统计特征值推断AI 解读

We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of the population covariance matrix are unknown and focus on inferential procedures that are based on the sample eigenvalues alone (i.e., “eigen-inference”). Results found in the literature establish the asymptotic normality of the…

利用随机矩阵理论估计高维协方差矩阵的谱AI 解读

Estimating the eigenvalues of a population covariance matrix from a sample covariance matrix is a problem of fundamental importance in multivariate statistics; the eigenvalues of covariance matrices play a key role in many widely used techniques, in particular in principal component analysis (PCA). In many modern data analysis problems, statisticians are faced with large datasets where the sample size, n, is of the same order of magnitude as the number of variables p. Random…

高维稀疏协方差矩阵的算子范数一致估计AI 解读

Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices X of dimension n×p, where p and n are both large. Results from random matrix theory show very clearly that in this setting, standard estimators like the sample covariance matrix perform in general very poorly. In this “large n, large p” setting, it is sometimes the case that practitioners are willing to assume…

基于特征筛减独立规则的高维分类AI 解读

Classification using high-dimensional features arises frequently in many contemporary statistical studies such as tumor classification using microarray or other high-throughput data. The impact of dimensionality on classifications is largely poorly understood. In a seminal paper, Bickel and Levina (2004) show that the Fisher discriminant performs poorly due to diverging spectra and they propose to use the independence rule to overcome the problem. We first demonstrate that…

正则化样本协方差矩阵的中心极限定理AI 解读

We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers (similar to that proved in the Gaussian case by Bickel and Levina), which implies that the spectrum of a banded empirical covariance matrix is an efficient estimator. Our main result is a central limit theorem in the same regime, which to our…

通过阈值化实现协方差正则化AI 解读

This paper considers regularizing a covariance matrix of p variables estimated from n observations, by hard thresholding. We show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense, the variables are Gaussian or sub-Gaussian, and (log p)/n→0, and obtain explicit rates. The results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity. We discuss an…

弹性估计的推断方法AI 解读

Elasticities are often estimated from the results of demand analysis. However, drawing inferences from them may involve assumptions that could influence the outcome. In this paper we investigate one of the most common forms of elasticity which is defined as a ratio of estimated relationships and demonstrate how the Fieller method for the construction of confidence intervals can be used to draw inferences. We estimate the elasticities of expenditure from Engel curves using a…

具有异方差误差的神经网络需求系统AI 解读

In this paper we consider estimation of demand systems with flexible functional forms, allowing an error term with a general conditional heteroskedasticity function that depends on observed covariates, such as demographic variables. We propose a general model that can be estimated either by quasi-maximum likelihood (in the case of exogenous regressors) or generalized method of moments (GMM) if the covariates are endogenous. The specification proposed in the paper nests…

需求估计的另一种方法：含条件波动的高频航空旅客到达量神经网络回归AI 解读

In this paper we provide an alternative approach to analyze the demand for international tourism in the Balearic Islands, Spain, by using a neural network model that incorporates time-varying conditional volatility. We consider daily air passenger arrivals to Palma de Mallorca, Ibiza and Mahon, which are located in the islands of Mallorca, Ibiza and Menorca, respectively, as a proxy for international tourism demand for the Balearic Islands. Spain is a world leader in terms…

大量非负约束绑定时的高维需求系统估计AI 解读

Two econometric issues arise in the structural estimation of consumer or producer demand systems in the presence of many binding non-negativity constraints. Firstly, most existing methods entail the evaluation of multivariate probability integrals. Secondly, the issue of statistical coherency must be addressed. We circumvent both of these issues using Gibbs' Sampling, along with data augmentation and rejection sampling. We illustrate our method using several simulated data…

超高维特征空间的确定性独立筛选AI 解读

Summary Variable selection plays an important role in high dimensional statistical modelling which nowadays appears in many areas and is key to various scientific discoveries. For problems of large scale or dimensionality p, accuracy of estimation and computational cost are two top concerns. Recently, Candes and Tao have proposed the Dantzig selector using L1-regularization and showed that it achieves the ideal risk up to a logarithmic factor log(p). Their innovative…

金融与风险管理中的计量建模：概览AI 解读

This paper gives an overview about the sixteen papers included in this special issue. The papers in this special issue cover a wide range of topics. Such topics include discussing a class of tests for correlation, estimation of realized volatility, modeling time series and continuous-time models with long-range dependence, estimation and specification testing of time series models, estimation in a factor model with high-dimensional problems, finite-sample examination of…

使用因子模型估计高维协方差矩阵AI 解读

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to [infinity] as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observable and the number of factors K is allowed to grow with p. We investigate…

Behrens–Fisher问题：全局收敛算法及Wald、LR与LM检验的有限样本研究AI 解读

In this paper we provide a provably convergent algorithm for the multivariate Gaussian Maximum Likelihood version of the Behrens–Fisher Problem. Our work builds upon a formulation of the log-likelihood function proposed by Buot and Richards [5]. Instead of focusing on the first order optimality conditions, the algorithm aims directly for the maximization of the log-likelihood function itself to achieve a global solution. Convergence proof and complexity estimates are…

高维分类与数据挖掘中的 Gibbs 后验变量选择AI 解读

In the popular approach of “Bayesian variable selection” (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a Gibbs posterior originating in statistical mechanics. The Gibbs posterior is constructed from a risk function of practical interest (such as the classification error) and aims at minimizing a risk function without modeling the data…

大型多方程马尔可夫切换模型的推断方法AI 解读

Inference for multiple-equation Markov-chain models raises a number of difficulties that are unlikely to appear in smaller models. Our framework allows for many regimes in the transition matrix, without letting the number of free parameters grow as the square as the number of regimes, but also without losing a convenient form for the posterior distribution. Calculation of marginal data densities is difficult in these high-dimensional models. This paper gives methods to…

利用主成分联合建模成对稀疏函数数据AI 解读

We propose a modelling framework to study the relationship between two paired longitudinally observed variables. The data for each variable are viewed as smooth curves measured at discrete time-points plus random errors. While the curves for each variable are summarized using a few important principal components, the association of the two longitudinal variables is modelled through the association of the principal component scores. We use penalized splines to model the mean…

大模型空间下用于模型选择的扩展贝叶斯信息准则AI 解读

The ordinary Bayesian information criterion is too liberal for model selection when the model space is large. In this paper, we re-examine the Bayesian paradigm for model selection and propose an extended family of Bayesian information criteria, which take into account both the number of unknown parameters and the complexity of the model space. Their consistency is established, in particular allowing the number of covariates to increase to infinity with the sample size.…