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非参数核检验中的带宽选择AI 解读

We propose a sound approach to bandwidth selection in nonparametric kernel testing. The main idea is to find an Edgeworth expansion of the asymptotic distribution of the test concerned. Due to the involvement of a kernel bandwidth in the leading term of the Edgeworth expansion, we are able to establish closed-form expressions to explicitly represent the leading terms of both the size and power functions and then determine how the bandwidth should be chosen according to…

祖细胞群体的分枝过程模型与后代分布估计AI 解读

We consider two new models of reducible age-dependent branching processes with emigration in conjunction with estimation problems arising in cell biology. Methods of statistical inference are developed using the relevant embedded discrete branching structure. Based on observations of the branching process with emigration, estimators of the offspring probabilities are proposed for the hidden unobservable process without emigration, which is of prime interest to investigators.…

高维稀疏因子建模：基因表达组学应用AI 解读

We describe studies in molecular profiling and biological pathway analysis that use sparse latent factor and regression models for microarray gene expression data. We discuss breast cancer applications and key aspects of the modeling and computational methodology. Our case studies aim to investigate and characterize heterogeneity of structure related to specific oncogenic pathways, as well as links between aggregate patterns in gene expression profiles and clinical…

利用贝叶斯广义线性模型评估疟疾抗原序列氨基酸位点的选择作用AI 解读

We present a statistical approach for identifying residues in DNA sequences for which diversity may be maintained by natural selection. Bayesian generalized linear models (GLMs) are used to describe patterns of mutation in a DNA sequence alignment. Posterior distributions of key quantities, such as probabilities of nonsynonymous and synonymous mutations per site, are studied. Inference in this class of models is achieved through customary Markov chain Monte Carlo methods.…

多指标模型与进一步降维AI 解读

Dimension reduction can be used as an initial step in statistical modeling. Further specification of model structure is imminent and important when the reduced dimension is still greater than 1. In this article we investigate one method of specification that involves separating the linear component from the nonlinear components, leading to further dimension reduction in the unknown link function and, thus, better estimation and easier interpretation of the model. The…

在回归测量误差框架下估计微分方程模型参数AI 解读

Differential equation (DE) models are widely used in many scientific fields that include engineering, physics and biomedical sciences. The so-called "forward problem", the problem of simulations and predictions of state variables for given parameter values in the DE models, has been extensively studied by mathematicians, physicists, engineers and other scientists. However, the "inverse problem", the problem of parameter estimation based on the measurements of output…

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…

纵向数据协方差矩阵的半参数估计AI 解读

Estimation of longitudinal data covariance structure poses significant challenges because the data are usually collected at irregular time points. A viable semiparametric model for covariance matrices was proposed in Fan, Huang and Li (2007) that allows one to estimate the variance function nonparametrically and to estimate the correlation function parametrically via aggregating information from irregular and sparse data points within each subject. However, the asymptotic…

非那雄胺是否影响前列腺癌严重程度：因果敏感性分析AI 解读

In 2003 Thompson and colleagues reported that daily use of finasteride reduced the prevalence of prostate cancer by 25% compared to placebo. These results were based on the double-blind randomized Prostate Cancer Prevention Trial (PCPT) which followed 18,882 men with no prior or current indications of prostate cancer annually for seven years. Enthusiasm for the risk reduction afforded by the chemopreventative agent and adoption of its use in clinical practice, however, was…

早期干预效果的多重推断与性别差异：三项实验的重新评估AI 解读

The view that the returns to educational investments are highest for early childhood interventions is widely held and stems primarily from several influential randomized trials—Abecedarian, Perry, and the Early Training Project—that point to super-normal returns to early interventions. This article presents a de novo analysis of these experiments, focusing on two core issues that have received limited attention in previous analyses: treatment effect heterogeneity by gender…

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…

高斯对称矩阵特征值与特征向量的推断AI 解读

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3×3 and 2×2 symmetric…

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…

多元分析与 Jacobi 系综：最大特征值、Tracy–Widom 极限及收敛速率AI 解读

Let A and B be independent, central Wishart matrices in p variables with common covariance and having m and n degrees of freedom, respectively. The distribution of the largest eigenvalue of (A + B)(-1)B has numerous applications in multivariate statistics, but is difficult to calculate exactly. Suppose that m and n grow in proportion to p. We show that after centering and, scaling, the distribution is approximated to second-order, O(p(-2/3)), by the Tracy-Widom law. The…

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…

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…

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…

消费者偏好弱可分性的非参数检验AI 解读

Two stochastic nonparametric procedures are developed to evaluate the significance of violations of weak separability. When the data have measurement error, we show that the necessary and sufficient weak separability conditions of Varian [Varian, H., 1983. Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99-110] must also satisfy the Afriat inequalities. The tests detect weak separability with high probability for weakly separable data. In addition,…

忽略耐用性导致的需求与供给估计偏误AI 解读

We build a dynamic equilibrium model of a durable goods oligopoly with a competitive secondary market to evaluate the bias in estimating the structural parameters of demand and supply when durability is omitted. We simulate data from our dynamic model and use them to estimate the model's static counterpart. We find that the static estimate of the elasticity of demand is an overestimate of the true elasticity and that the static estimate of the markup is an underestimate. Our…

集体理性消费行为的非参数检验：整数规划程序AI 解读

We present an IP-based nonparametric (revealed preference) testing procedure for rational consumption behavior in terms of a general collective model, which includes consumption externalities and public consumption. An empirical application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the practical usefulness of the procedure. Finally, we present extensions of the testing procedure to evaluate the goodness-of-fit (accounting for…

利用恩格尔曲线估计集体家庭模型AI 解读

The structural consumer demand methods used to estimate the parameters of collective household models are typically either very restrictive and easy to implement or very general and difficult to estimate. In this paper, we provide a middle ground. We adapt the very general framework of [Browning, M., Chiappori, P.A., Lewbel, A., 2004. Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power, Boston College Working Papers in…

门限自回归中的单位根检验：渐近理论与残差区块自助法AI 解读

This paper develops a test of the unit root null hypothesis against a stationary threshold process. This testing problem is nonstandard and complicated because a parameter is unidentified and the process is nonstationary under the null hypothesis. We derive an asymptotic distribution for the test, which is not pivotal without simplifying assumptions. A residual-based block bootstrap is proposed to calculate the asymptotic p -values. The asymptotic validity of the bootstrap…