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超对冲价格的稳健估计AI 解读

We consider statistical estimation of superhedging prices using historical stock returns in a frictionless market with $d$ traded assets. We introduce a plug-in estimator based on empirical measures and show it is consistent but lacks suitable robustness. To address this, we propose novel estimators which use a larger set of martingale measures defined through a tradeoff between the radius of Wasserstein balls around the empirical measure and the allowed norm of martingale…

非对称性的益处：非对称扰动低秩矩阵的特征值与特征向量分析AI 解读

This paper is concerned with the interplay between statistical asymmetry and spectral methods. Suppose we are interested in estimating a rank-1 and symmetric matrix $\boldsymbol{M}^{\star }\in \mathbb{R}^{n\times n}$, yet only a randomly perturbed version $\boldsymbol{M}$ is observed. The noise matrix $\boldsymbol{M}-\boldsymbol{M}^{\star }$ is composed of independent (but not necessarily homoscedastic) entries and is, therefore, not symmetric in general. This might arise…

球面函数自回归的渐近理论AI 解读

In this paper, we investigate a class of spherical functional autoregressive processes, and we discuss the estimation of the corresponding autoregressive kernels. In particular, we first establish a consistency result (in mean-square and sup norm), then a quantitative central limit theorem (in Wasserstein distance), and finally a weak convergence result, under more restrictive regularity conditions. Our results are validated by a small numerical investigation.

多元时间序列极值中的多重块长与重叠分块AI 解读

Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations from a genuine extreme value distribution. In practice, however, block sizes are finite and observations from different blocks are dependent. Theory respecting the latter complications is not well developed, and, in the multivariate case,…

伴随异常值筛选的最小效应估计AI 解读

We introduce one-sided versions of Huber’s contamination model, in which corrupted samples tend to take larger values than uncorrupted ones. Two intertwined problems are addressed: estimation of the mean of the uncorrupted samples (minimum effect) and selection of the corrupted samples (outliers). Regarding estimation of the minimum effect, we derive the minimax risks and introduce estimators that are adaptive with respect to the unknown number of contaminations. The optimal…

高维检验中渐近独立的U统计量AI 解读

Many high-dimensional hypothesis tests aim to globally examine marginal or low-dimensional features of a high-dimensional joint distribution, such as testing of mean vectors, covariance matrices and regression coefficients. This paper constructs a family of U-statistics as unbiased estimators of the $\ell_{p}$-norms of those features. We show that under the null hypothesis, the U-statistics of different finite orders are asymptotically independent and normally distributed.…

多元对数凹密度估计的自适应性AI 解读

We study the adaptation properties of the multivariate log-concave maximum likelihood estimator over three subclasses of log-concave densities. The first consists of densities with polyhedral support whose logarithms are piecewise affine. The complexity of such densities $f$ can be measured in terms of the sum $\Gamma(f)$ of the numbers of facets of the subdomains in the polyhedral subdivision of the support induced by $f$. Given $n$ independent observations from a $d$-dimens…

噪声观测下兼具统计最优性与计算效率的低秩张量补全AI 解读

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of noisy tensor completion. Much of the attention has been focused on the fundamental computational challenges often associated with problems involving higher order tensors, yet very little is known about their statistical performance. To…

最优治疗决策的一致性与价值信息准则AI 解读

Personalized medicine is a medical procedure that receives considerable scientific and commercial attention. The goal of personalized medicine is to assign the optimal treatment regime for each individual patient, according to his/her personal prognostic information. When there are a large number of pretreatment variables, it is crucial to identify those important variables that are necessary for treatment decision making. In this paper, we study two information criteria:…

The central subspace of a pair of random variables $(y,\boldsymbol{x})\in \mathbb{R}^{p+1}$ is the minimal subspace $\mathcal{S}$ such that $y\perp\!\!\!\!\!\perp \boldsymbol{x}|P_{\mathcal{S}}\boldsymbol{x}$. In this paper, we consider the minimax rate of estimating the central space under the multiple index model $y=f(\boldsymbol{\beta }_{1}^{\tau }\boldsymbol{x},\boldsymbol{\beta }_{2}^{\tau }\boldsymbol{x},\ldots,\boldsymbol{\beta }_{d}^{\tau }\boldsymbol{x},\epsilon )$ w…

复杂抽样设计：一致极限定理及其应用AI 解读

In this paper, we develop a general approach to proving global and local uniform limit theorems for the Horvitz–Thompson empirical process arising from complex sampling designs. Global theorems such as Glivenko–Cantelli and Donsker theorems, and local theorems such as local asymptotic modulus and related ratio-type limit theorems are proved for both the Horvitz–Thompson empirical process, and its calibrated version. Limit theorems of other variants and their conditional…

稳健多元均值估计：截尾均值的最优性AI 解读

We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal conditions.

利用近似消息传递估计低秩矩阵AI 解读

Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise, a setting that is also known as “spiked model” or “deformed random matrix.” If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic accuracy of Bayes-optimal estimators in the high-dimensional limit. In this paper, we…

高维局部平稳过程的协方差与谱密度估计收敛性AI 解读

Covariances and spectral density functions play a fundamental role in the theory of time series. There is a well-developed asymptotic theory for their estimates for low-dimensional stationary processes. For high-dimensional nonstationary processes, however, many important problems on their asymptotic behaviors are still unanswered. This paper presents a systematic asymptotic theory for the estimates of time-varying second-order statistics for a general class of…

稀疏动态网络中变点的最优检测与定位AI 解读

We study the problem of change point localization in dynamic networks models. We assume that we observe a sequence of independent adjacency matrices of the same size, each corresponding to a realization of an unknown inhomogeneous Bernoulli model. The underlying distribution of the adjacency matrices are piecewise constant, and may change over a subset of the time points, called change points. We are concerned with recovering the unknown number and positions of the change…

非参数分类的迁移学习：极小极大速率与自适应分类器AI 解读

Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper, we study transfer learning in the context of nonparametric classification based on observations from different distributions under the posterior drift model, which is a general framework and arises in many practical problems. We first…

具有多重结构变化的高维因子模型估计与检验AI 解读

This paper considers multiple changes in the factor loadings of a high dimensional factor model occurring at dates that are unknown but common to all subjects. Since the factors are unobservable, the problem is converted to estimating and testing structural changes in the second moments of the pseudo factors. We consider both joint and sequential estimation of the change points and show that the distance between the estimated and the true change points is Op(1). We find that…

合并 CCE 估计量的稳健性AI 解读

Among the existing estimators of factor-augmented regressions, the CCE approach is the most popular. A major reason for this popularity is the simplicity and good small-sample performance of the approach, making it very attractive from an empirical point of view. The main drawback is that most of the available asymptotic theory is based on quite restrictive assumptions, such as that the common factor component should be independent of the regressors. The present paper can be…

去因子回归变量与多因子误差下的动态线性面板工具变量估计AI 解读

This paper develops two instrumental variable (IV) estimators for dynamic panel data models with exogenous covariates and a multifactor error structure when both the cross-sectional and time series dimensions, N and T respectively, are large. The main idea is to project out the common factors from the exogenous covariates of the model, and to construct instruments based on defactored covariates. For models with homogeneous slope coefficients, we propose a two-step IV…

含 MIDAS 协变量的动态面板：非线性、估计与拟合AI 解读

This paper introduces Mixed Data Sampling (MIDAS) into the panel data context. To address the unidentified nuisance parameter problem, we propose to invert model specification tests for inference on the MIDAS parameter along with bounds tests for model coefficients. Illustrative identification, simulation and empirical analyses are conducted in the dynamic GMM framework. Our framework allows for departures from i.i.d errors such as clustering and dynamic specifications. A…

网络与面板数据的非线性因子模型AI 解读

Factor structures or interactive effects are convenient devices to incorporate latent variables in panel data models. We consider fixed effect estimation of nonlinear panel single-index models with factor structures in the unobservables, which include logit, probit, ordered probit and Poisson specifications. We establish that fixed effect estimators of model parameters and average partial effects have normal distributions when the two dimensions of the panel grow large, but…

结合横截面与时间序列信息的债券价格非参数估计AI 解读

We develop a novel estimation methodology for an additive nonparametric panel model that is suitable for capturing the pricing of coupon-paying government bonds followed over many time periods. We use our model to estimate the discount function and yield curve of nominally riskless government bonds. The novelty of our approach is the combination of two different techniques: cross-sectional nonparametric methods and kernel estimation for time varying dynamics in the time…

层级多因子误差下多维异质面板的估计与推断AI 解读

Given the growing availability of large datasets and following recent research trends on multi-dimensional modelling, we develop three dimensional (3D) panel data models with hierarchical error components that allow for strong cross-section dependence through unobserved heterogeneous global and local factors. We propose consistent estimation procedures by extending the common correlated effects (CCE) estimation approach proposed by Pesaran (2006). The standard CCE approach…

非线性面板中潜在分组结构的识别AI 解读

We propose a procedure to identify latent group structures in nonlinear panel data models where some regression coefficients are heterogeneous across groups but homogeneous within a group and the group number and membership are unknown. To identify the group structures, we consider the order statistics for the preliminary unconstrained consistent estimators of the regression coefficients and translate the problem of classification into the problem of break detection. Then we…