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微生物群落分析的贝叶斯非参数排序方法AI 解读

Human microbiome studies use sequencing technologies to measure the abundance of bacterial species or Operational Taxonomic Units (OTUs) in samples of biological material. Typically the data are organized in contingency tables with OTU counts across heterogeneous biological samples. In the microbial ecology community, ordination methods are frequently used to investigate latent factors or clusters that capture and describe variations of OTU counts across biological samples.…

多变量季节调整、经济恒等式与季节性分类AI 解读

This article extends the methodology for multivariate seasonal adjustment by exploring the statistical modeling of seasonality jointly across multiple time series, using latent dynamic factor models fitted using maximum likelihood estimation. Signal extraction methods for the series then allow us to calculate a model-based seasonal adjustment. We emphasize several facets of our analysis: (i) we quantify the efficiency gain in multivariate signal extraction versus univariate…

稀疏混合模型中的检测与特征选择AI 解读

We consider Gaussian mixture models in high dimensions, focusing on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive minimax rates for the problems of testing and of variable selection. We find these rates to depend crucially on the knowledge of the covariance matrices and on whether the mixture is symmetric or not. We establish the performance of various procedures, including the top sparse eigenvalue of the…

高维聚类及相关问题的相变AI 解读

Consider a two-class clustering problem where we observe $X_{i}=\ell_{i}\mu+Z_{i}$, $Z_{i}\stackrel{\mathit{i.i.d.}}{\sim}N(0,I_{p})$, $1\leq i\leq n$. The feature vector $\mu\in R^{p}$ is unknown but is presumably sparse. The class labels $\ell_{i}\in\{-1,1\}$ are also unknown and the main interest is to estimate them. We are interested in the statistical limits. In the two-dimensional phase space calibrating the rarity and strengths of useful features, we find the precise…

稀疏典型相关分析：自适应估计与计算障碍AI 解读

Canonical correlation analysis is a classical technique for exploring the relationship between two sets of variables. It has important applications in analyzing high dimensional datasets originated from genomics, imaging and other fields. This paper considers adaptive minimax and computationally tractable estimation of leading sparse canonical coefficient vectors in high dimensions. Under a Gaussian canonical pair model, we first establish separate minimax estimation rates…

可扩展因子分析AI 解读

Bayesian sparse factor models have proven useful for characterizing dependence in multivariate data, but scaling computation to large numbers of samples and dimensions is problematic. We propose expandable factor analysis for scalable inference in factor models when the number of factors is unknown. The method relies on a continuous shrinkage prior for efficient maximum a posteriori estimation of a low-rank and sparse loadings matrix. The structure of the prior leads to an…

未知依赖结构下的错误发现比例估计AI 解读

Summary Large-scale multiple testing with correlated test statistics arises frequently in much scientific research. Incorporating correlation information in approximating the false discovery proportion (FDP) has attracted increasing attention in recent years. When the covariance matrix of test statistics is known, Fan and his colleagues provided an accurate approximation of the FDP under arbitrary dependence structure and some sparsity assumption. However, the covariance…

利用大型协方差矩阵对交互效应面板模型进行推断AI 解读

We consider efficient estimation of panel data models with interactive effects, which relies on a high-dimensional inverse covariance matrix estimator. By using a consistent estimator of the error covariance matrix, we can take into account both cross-sectional correlations and heteroskedasticity. In the presence of cross-sectional correlations, the proposed estimator eliminates the cross-sectional correlation bias, and is more efficient than the existing methods. The rate…

结构 FECM：大规模结构 FAVAR 模型中的协整AI 解读

Summary Starting from the dynamic factor model for nonstationary data we derive the factor‐augmented error correction model (FECM) and its moving‐average representation. The latter is used for the identification of structural shocks and their propagation mechanisms. We show how to implement classical identification schemes based on long‐run restrictions in the case of large panels. The importance of the error correction mechanism for impulse response analysis is analyzed by…

兼具时间与横截面依赖的因子模型的有效估计AI 解读

Summary This paper studies the efficient estimation of large‐dimensional factor models with both time and cross‐sectional dependence assuming ( N , T ) separability of the covariance matrix. The asymptotic distribution of the estimator of the factor and factor‐loading space under factor stationarity is derived and compared to that of the principal component (PC) estimator. The paper also considers the case when factors exhibit a unit root. We provide feasible estimators and…

识别稀疏因子模型中对因子估计有用与无用的变量AI 解读

Summary This paper considers factor estimation from heterogeneous data, where some of the variables—the relevant ones—are informative for estimating the factors, and others—the irrelevant ones—are not. We estimate the factor model within a Bayesian framework, specifying a sparse prior distribution for the factor loadings. Based on identified posterior factor loading estimates, we provide alternative methods to identify relevant and irrelevant variables. Simulations show that…

使用估计因子与特异成分的模型选择AI 解读

Summary This paper provides consistent information criteria for the selection of forecasting models that use a subset of both the idiosyncratic and common factor components of a big dataset. This hybrid model approach has been explored by recent empirical studies to relax the strictness of pure factor‐augmented model approximations, but no formal model selection procedures have been developed. The main difference to previous factor‐augmented model selection procedures is…

相关结构下PCA的精细检测：所有特征值都重要AI 解读

Principal component analysis (PCA) is a widely used method for dimension reduction. In high-dimensional data, the “signal” eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the “noise” eigenvalues. Therefore, popular tests based on the largest eigenvalue have little power to detect weak PCs. In the special case of the spiked model, certain tests asymptotically equivalent to linear spectral statistics (LSS)—averaging…

大型噪声矩阵中子矩阵定位的计算与统计边界AI 解读

We study in this paper computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple nonoverlapping) signal submatrix (of magnitude $\lambda$ and size $k_{m}\times k_{n}$) embedded in a large noise matrix (of size $m\times n$), the goal is to optimal identify the support of the signal submatrix computationally and statistically. Two transition thresholds for the signal-to-noise ratio $\lambda/\sigma$ are established in terms…

面向公开报告的死亡率估计与标准化：Medicare 医院比较AI 解读

Bayesian models are increasingly fit to large administrative datasets and then used to make individualized recommendations. In particular, Medicare’s Hospital Compare webpage provides information to patients about specific hospital mortality rates for a heart attack or acute myocardial infarction (AMI). Hospital Compare’s current recommendations are based on a random-effects logit model with a random hospital indicator and patient risk factors. Except for the largest…

纵向研究中基因与环境交互的集合检验AI 解读

We propose a generalized score type test for set-based inference for gene-environment interaction with longitudinally measured quantitative traits. The test is robust to misspecification of within subject correlation structure and has enhanced power compared to existing alternatives. Unlike tests for marginal genetic association, set-based tests for gene-environment interaction face the challenges of a potentially misspecified and high-dimensional main effect model under the…

MWPCR：用于高维预测的多尺度加权主成分回归AI 解读

We propose a multiscale weighted principal component regression (MWPCR) framework for the use of high dimensional features with strong spatial features (e.g., smoothness and correlation) to predict an outcome variable, such as disease status. This development is motivated by identifying imaging biomarkers that could potentially aid detection, diagnosis, assessment of prognosis, prediction of response to treatment, and monitoring of disease status, among many others. The…

海量金融时间序列聚类：高维预测变量与因子结构的面板方法AI 解读

This article introduces a new procedure for clustering a large number of financial time series based on high-dimensional panel data with grouped factor structures. The proposed method attempts to capture the level of similarity of each of the time series based on sensitivity to observable factors as well as to the unobservable factor structure. The proposed method allows for correlations between observable and unobservable factors and also allows for cross-sectional and…

具有稀疏载荷的扩散指数AI 解读

The use of large-dimensional factor models in forecasting has received much attention in the literature with the consensus being that improvements on forecasts can be achieved when comparing with standard models. However, recent contributions in the literature have demonstrated that care needs to be taken when choosing which variables to include in the model. A number of different approaches to determining these variables have been put forward. These are, however, often…

无限维因子空间动态因子模型的渐近分析AI 解读

Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni et al., (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni et al. (2004). Those estimators, however, rely on Brillinger’s concept of dynamic principal components, and thus involve two-sided filters, which leads to…

动态因子模型的经验贝叶斯方法AI 解读

We consider the dynamic factor model where the loading matrix, the dynamic factors, and the disturbances are treated as latent stochastic processes. We present empirical Bayes methods that enable the shrinkagebased estimation of the loadings and factors. We investigate the methods in a large Monte Carlo study where we evaluate the finite sample properties of the empirical Bayes methods for quadratic loss functions. Finally, we present and discuss the results of an empirical…

通过系数调整改进并显式化代理变量分析AI 解读

Unobserved environmental, demographic and technical factors canadversely affect the estimation and testing of the effects ofprimary variables. Surrogate variable analysis, proposed to tacklethis problem, has been widely used in genomic studies. To estimatehidden factors that are correlated with the primary variables,surrogate variable analysis performs principal component analysiseither on a subset of features or on all features, but weightingeach differently. However,…

高维相关矩阵：中心极限定理及其应用AI 解读

Summary Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, the paper establishes a new central limit theorem for a linear spectral statistic of high dimensional sample correlation matrices for the case where the dimension p and the sample size n are comparable. This result is of independent interest in large dimensional random-matrix theory. We also further investigate the sample correlation matrices of…

高维尖峰协方差经验特征结构的渐近理论AI 解读

We derive the asymptotic distributions of the spiked eigenvalues and eigenvectors under a generalized and unified asymptotic regime, which takes into account the magnitude of spiked eigenvalues, sample size, and dimensionality. This regime allows high dimensionality and diverging eigenvalues and provides new insights into the roles that the leading eigenvalues, sample size, and dimensionality play in principal component analysis. Our results are a natural extension of those…