论文检索

以分类准确率作为两样本检验的替代依据AI 解读

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the high-dimensional setting. We prove two results that hold for all classifiers in any dimensions: if its true error remains $\epsilon $-better than chance for some $\epsilon >0$ as $d,n\to \infty $, then (a) the permutation-based test is consistent…

矩阵去噪模型中的奇异向量与奇异子空间分布AI 解读

In this paper, we study the matrix denoising model $Y=S+X$, where $S$ is a low rank deterministic signal matrix and $X$ is a random noise matrix, and both are $M\times n$. In the scenario that $M$ and $n$ are comparably large and the signals are supercritical, we study the fluctuation of the outlier singular vectors of $Y$, under fully general assumptions on the structure of $S$ and the distribution of $X$. More specifically, we derive the limiting distribution of angles…

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…

贝叶斯极限的频率学有效性AI 解读

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper, a Bayesian perspective on test sequences is proposed and Schwartz’s Kullback–Leibler condition is generalised to widen the range of frequentist applications of posterior convergence. With Bayesian tests and a weakened form of contiguity termed remote contiguity, we prove simple and fully general frequentist theorems, for posterior consistency and rates of convergence, for…

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.…

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:…

使用 jackknife+ 的预测推断AI 解读

This paper introduces the jackknife+, which is a novel method for constructing predictive confidence intervals. Whereas the jackknife outputs an interval centered at the predicted response of a test point, with the width of the interval determined by the quantiles of leave-one-out residuals, the jackknife+ also uses the leave-one-out predictions at the test point to account for the variability in the fitted regression function. Assuming exchangeable training samples, we…

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…

随机优化中的渐近最优性AI 解读

We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our results provide function-specific lower bounds and convergence results that make precise a correspondence between statistical difficulty and the geometric…

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…

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…

非线性固定效应面板模型的二阶似然修正AI 解读

We propose a second-order correction for nonlinear fixed-effect panel models. The correction is made via the log-likelihood function. It removes the two leading terms of the bias of the log-likelihood that arises from estimating the fixed effects. Maximizing the corrected likelihood gives a second-order bias-corrected estimator, with bias OT−3, where T is the number of time periods. The corrected likelihood also gives second-order corrected test statistics. The correction…

大规模面板中异质性与协整的推断理论AI 解读

This paper provides an estimation and testing framework to assess the presence and the extent of slope heterogeneity and cointegration when the units are a mixture of spurious and/or cointegrating regressions. We propose two moment estimators for the degree of heterogeneity (measured by the dispersion of the slope coefficients around their average) and for the fraction of spurious regressions, which are found to be consistent in the whole parameter space. Based on these…

多层模型估计的计量经济学方法AI 解读

In this paper we consider “multidimensional” or “hierarchical” or “multilevel” models that are popular in the educational and economics literatures. Instead of two levels (individuals over time in the standard panel data model), we now have multiple levels (e.g. students in classrooms in schools in districts). We apply standard methods of analysis for econometric panel data to multilevel models. Specifically, we generalize the results of Hausman and Taylor and the subsequent…

具有系统性斜率变化的异质面板估计AI 解读

We analyse estimation procedures for the panel data models with heterogeneous slopes. Specifically we take into account a possible dependence between regressors and heterogeneous slope coefficients, which is referred to as systematic variation. It is shown that under relevant forms of systematic slope variations (i) the pooled OLS estimator is severely biased, (ii) Swamy’s GLS estimator is inconsistent if the number of time periods T is fixed, whereas (iii) the mean-group…

近单位根回归变量下的近最优长期可预测性检验AI 解读

We develop a method for long-run predictability testing in series Y by a persistent series X. We consider a class of tests based on the long-run behavior of these series that are robust to short-run dynamics and attempt to attain the highest possible power. The test is based on the Whittle approximation to the likelihood ratio that is adjusted to remain accurate across a range of persistence in X . We verify the properties of this test in small simulations and compare this…