论文检索

高维广义因子模型的极大似然估计与推断：因子扩展回归应用AI 解读

This paper reestablishes the main results in Bai (2003) and Bai and Ng (2006) for generalized factor models, with slightly stronger conditions on the relative magnitude of N (number of subjects) and T (number of time periods). Convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear, Logit, Probit, Tobit, Poisson and some other single-index…

大数据时代的市场有效性AI 解读

Modern investors face a high-dimensional prediction problem: thousands of observable variables are potentially relevant for forecasting. We reassess the conventional wisdom on market efficiency in light of this fact. In our equilibrium model, N assets have cash flows that are linear in J characteristics, with unknown coefficients. Risk-neutral Bayesian investors learn these coefficients and determine market prices. If J and N are comparable in size, returns are…

货币政策沟通及其对家庭通胀预期的影响AI 解读

We study how different forms of communication influence inflation expectations in a randomized controlled trial using nearly 20,000 US individuals. We elicit individuals’ inflation expectations and then provide eight different forms of information regarding inflation. Reading the actual Federal Open Market Committee (FOMC) statement has about the same average effect on expectations as simply being told about the Federal Reserve’s inflation target. Reading news articles about…

基于成对比较的最优完整排序AI 解读

We consider the problem of ranking n players from partial pairwise comparison data under the Bradley–Terry–Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendall’s tau distance that measures the difference between two rank vectors by counting the number of inversions. The minimax rate of ranking exhibits a transition between an exponential rate and a polynomial rate depending on the magnitude of the…

具有对称不变性的高斯模型空间中的模型选择AI 解读

We consider multivariate centered Gaussian models for the random variable Z=(Z1,…,Zp), invariant under the action of a subgroup of the group of permutations on {1,…,p}. Using the representation theory of the symmetric group on the field of reals, we derive the distribution of the maximum likelihood estimate of the covariance parameter Σ and also the analytic expression of the normalizing constant of the Diaconis–Ylvisaker conjugate prior for the precision parameter K=Σ−1. We…

基于计数数据的 Hawkes 过程谱估计AI 解读

This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood are not feasible. We show that spectral estimation based on Whittle’s method is adapted to this case and provides consistent and asymptotically normal estimators, provided a mild moment condition on the reproduction function. Simulated…

稀疏纵向观测的内蕴黎曼函数型数据分析AI 解读

A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a parallel transport and a smooth bundle metric on the covariance vector bundle. The introduced intrinsic covariance function links estimation of covariance structure to smoothing problems that involve raw covariance observations derived from…

Boosting 与最小 ℓ1 范数插值分类器的精确高维渐近理论AI 解读

This paper establishes a precise high-dimensional asymptotic theory for boosting on separable data, taking statistical and computational perspectives. We consider a high-dimensional setting where the number of features (weak learners) p scales with the sample size n, in an overparametrized regime. Under a class of statistical models, we provide an exact analysis of the generalization error of boosting when the algorithm interpolates the training data and maximizes the…

形状约束下密度水平集估计的数据自适应方法AI 解读

Given a random sample of points from some unknown density, we propose a method for estimating density level sets, for a positive threshold t, under the r-convexity assumption. This shape condition generalizes the convexity property and allows to consider level sets with more than one connected component. The main problem in practice is that r is an unknown geometric characteristic of the set related to its curvature, which may depend on t. A stochastic algorithm is proposed…

大型 VAR 中的协整AI 解读

The paper analyzes cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, N, and the number of time periods, T, are large and of the same order. We propose a way to examine a VAR of order 1 for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from…

具有块结构的大规模统计推断AI 解读

The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale multiple testing that is inherent in these problems. Here, we show that fundamentally more powerful statistical inference is possible when there is some structure in the signal that can be exploited, for example, if the signal is clustered in…

Wasserstein 距离下光滑密度的极小极大估计AI 解读

We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates for this problem for general Wasserstein distances for two classes of densities: smooth probability densities on [0,1]d bounded away from 0, and sub-Gaussian densities lying in the Hölder class Cs, s∈(0,1). Unlike classical nonparametric…

多元最大稳定分布贝叶斯推断的一致性AI 解读

Predicting extreme events is important in many applications in risk analysis. Extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction. Although various Bayesian inferential procedures have been proposed in the literature of univariate extremes and some for multivariate extremes, the study of their asymptotic properties has been left largely untouched. In this paper we focus on…

用高阶批判检验比较大型频数表中的稀疏微弱差异AI 解读

We adapt Higher Criticism (HC) to the comparison of two frequency tables which may—or may not—exhibit moderate differences between the tables in some unknown, relatively small subset out of a large number of categories. Our analysis of the power of the proposed HC test quantifies the rarity and size of assumed differences and applies moderate deviations-analysis to determine the asymptotic powerfulness/powerlessness of our proposed HC procedure. Our analysis considers the…

密度水平集经验估计量的立方根弱收敛AI 解读

Given n independent random vectors with common density f on Rd, we study the weak convergence of three empirical-measure based estimators of the convex λ-level set Lλ of f, namely the excess mass set, the minimum volume set and the maximum probability set, all selected from a class of convex sets A that contains Lλ. Since these set-valued estimators approach Lλ, even the formulation of their weak convergence is nonstandard. We identify the joint limiting distribution of the…

重新审视岭回归：去偏、阈值化与自助法AI 解读

The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, that is, zeroing out regression coefficients that are not significant. By contrast, classical ridge regression cannot reveal a potential sparsity of parameters, and may also introduce a large bias under the high-dimensional setting. Nevertheless, recent work on the Lasso involves debiasing and thresholding, the latter in order to further enhance the…

部分线性Cox模型的深度学习方法AI 解读

While deep learning approaches to survival data have demonstrated empirical success in applications, most of these methods are difficult to interpret and mathematical understanding of them is lacking. This paper studies the partially linear Cox model, where the nonlinear component of the model is implemented using a deep neural network. The proposed approach is flexible and able to circumvent the curse of dimensionality, yet it facilitates interpretability of the effects of…

ARFIMA 过程的一致阶数选择AI 解读

Estimating the orders of the autoregressive fractionally integrated moving average (ARFIMA) model has been a long-standing problem in time series analysis. This paper tackles this challenge by establishing the consistency of the Bayesian information criterion (BIC) for ARFIMA models with independent errors. Since the memory parameter of the model can be any real number, this consistency result is valid for short memory, long memory and nonstationary time series. This paper…

利用多个可能无效的工具变量构造证据因子AI 解读

Valid instrumental variables enable treatment effect inference even when selection into treatment is biased by unobserved confounders. When multiple candidate instruments are available, but some of them are possibly invalid, the previously proposed reinforced design enables one or more nearly independent valid analyses that depend on very different assumptions. That is, we can perform evidence factor analysis. However, the validity of the reinforced design depends crucially…

多因素实验中的设计可容许性与 de la Garza 现象AI 解读

The determination of an optimal design for a given regression problem is an intricate optimization problem, especially for models with multivariate predictors. Design admissibility and invariance are main tools to reduce the complexity of the optimization problem and have been successfully applied for models with univariate predictors. In particular, several authors have developed sufficient conditions for the existence of minimally supported designs in univariate models,…

低次多项式估计的计算障碍AI 解读

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for such problems: it has been demonstrated in various settings that low-degree polynomials of the data can match the statistical performance of the best known polynomial-time algorithms. Prior work has studied the power of low-degree…

奇异信息与参数边界附近的置信域及其混合模型应用AI 解读

We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable inference on scale parameters close or equal to zero in mixed models, which is obtained as a special case. The confidence regions are constructed by inverting a continuous extension of the score test statistic standardized by expected…

前 k 名排序的部分恢复：极大似然最优性与谱方法的次优性AI 解读

Given partially observed pairwise comparison data generated by the Bradley–Terry–Luce (BTL) model, we study the problem of top-k ranking. That is, to optimally identify the set of top-k players. We derive the minimax rate with respect to a normalized Hamming loss. This provides the first result in the literature that characterizes the partial recovery error in terms of the proportion of mistakes for top-k ranking. We also derive the optimal signal to noise ratio condition…

局部弗雷歇回归的一致收敛及其在极值定位与时间配准中的应用AI 解读

Local Fréchet regression is a nonparametric regression method for metric space valued responses and Euclidean predictors, which can be utilized to obtain estimates of smooth trajectories taking values in general metric spaces from noisy metric space valued random objects. We derive uniform rates of convergence, which so far have eluded theoretical analysis of this method, for both fixed and random target trajectories, where we utilize tools from empirical processes. These…