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通过非参数极大似然实现多元异方差经验贝叶斯估计AI 解读

Abstract Multivariate, heteroscedastic errors complicate statistical inference in many large-scale denoizing problems. Empirical Bayes is attractive in such settings, but standard parametric approaches rest on assumptions about the form of the prior distribution which can be hard to justify and which introduce unnecessary tuning parameters. We extend the nonparametric maximum-likelihood estimator (NPMLE) for Gaussian location mixture densities to allow for multivariate,…

强化学习框架下的多变量动态中介分析AI 解读

Mediation analysis is an important analytic tool commonly used in a broad range of scientific applications. In this article, we study the problem of mediation analysis when there are multivariate and conditionally dependent mediators, and when the variables are observed over multiple time points. The problem is challenging, because the effect of a mediator involves not only the path from the treatment to this mediator itself at the current time point, but also all possible…

计算高效且统计最优的稳健高维线性回归AI 解读

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since the robust loss functions are usually nonsmooth. More recently, computationally fast nonconvex approaches via subgradient descent are proposed, which, unfortunately, fail to deliver a statistically consistent estimator even…

基于经验似然的多元正则变差检验AI 解读

Multivariate regular variation is a common assumption in the statistics literature and needs to be verified in real-data applications. We develop a novel hypothesis test for multivariate regular variation, employing localized empirical likelihood. We establish the weak convergence of the test statistic to a nonstandard, distribution-free limit and hence can provide universal critical values for the test. We show the very good finite-sample behavior of the procedure through…

大语言模型水印的统计框架：枢轴量、检测效率与最优规则AI 解读

Since ChatGPT was introduced in November 2022, embedding (nearly) unnoticeable statistical signals into text generated by large language models (LLMs), also known as watermarking, has been used as a principled approach to provable detection of LLM-generated text from its human-written counterpart. In this paper, we introduce a general and flexible framework for reasoning about the statistical efficiency of watermarks and designing powerful detection rules. Inspired by the…

非参数回归中的最优异方差检验AI 解读

Heteroskedasticity testing in nonparametric regression is a classic statistical problem with important practical applications, yet fundamental limits are unknown. Adopting a minimax perspective, this article considers the testing problem in the context of an α-Hölder mean and a β-Hölder variance function. For α>0 and β∈(0,1/2), the sharp minimax separation rate n−4α+n−4β/(4β+1)+n−2β is established. To achieve the minimax separation rate, a kernel-based statistic using…

格点上高维随机场的一般时空因子模型AI 解读

Motivated by the need for analysing large spatio-temporal panel data, we introduce a novel nonparametric methodology for n-dimensional random fields observed across S spatial locations and T time periods. We call it general spatio-temporal factor model (GSTFM). First, we provide the probabilistic and mathematical underpinning needed for the representation of a random field as the sum of two components: the common component (driven by a small number q of latent factors) and…

关于两个响应变量交互关系的有效降维理论AI 解读

Efficient dimension reduction regarding the interaction between two response variables, which facilitates statistical analysis in multiple important application scenarios, was initially discussed by Luo (J. R. Stat. Soc. Ser. B. Stat. Methodol. 84 (2022) 269–294). The efficient dimension reduction subspaces were introduced, and, under mild conditions on the predictor, they were equated with the family of dual inverse regression subspaces. Besides the general framework,…

混合半鞅的速率最优估计AI 解读

Consider the sum Y = B + B(H) of a Brownian motion B and an independent fractional Brownian motion B(H) with Hurst parameter H ∈ (0, 1). Even though B(H) is not a semimartingale, it was shown by Cheridito (Bernoulli 7 (2001) 913–934) that Y is a semimartingale if H > 3/4. Moreover, Y is locally equivalent to B in this case, so H cannot be consistently estimated from local observations of Y. This paper pivots on another unexpected feature in this model: if B and B(H) become…

一般非参数回归的集成投影寻踪AI 解读

Projection pursuit regression (PPR) and artificial neural networks (ANNs), both introduced around the same time, share a similar approach to approximating complex structures in data. However, PPR has received far less attention than ANNs and other popular statistical learning methods such as random forests (RF) and support vector machines (SVM). In this paper, we revisit the estimation of PPR and propose an optimal greedy algorithm and an ensemble approach via feature…

不交叉的单纯形分位数回归AI 解读

Noncrossing quantile regression with an emphasis on model misspecification is investigated. While many sophisticated methods for noncrossing quantile have been developed under the assumption of correct model specification, model misspecification and extrapolation are two issues rarely considered in the literature. In this paper, a monotonicity representation for quantile regression models is obtained under simplex embedding, which leads to the simplex quantile regression…

Deflated HeteroPCA：克服异方差主成分分析中的病态条件数问题AI 解读

This paper is concerned with estimating the column subspace of a low-rank matrix $\boldsymbol{X}^\star \in \mathbb{R}^{n_1\times n_2}$ from contaminated data. How to obtain optimal statistical accuracy while accommodating the widest range of signal-to-noise ratios (SNRs) becomes particularly challenging in the presence of heteroskedastic noise and unbalanced dimensionality (i.e., $n_2\gg n_1$). While the state-of-the-art algorithm $\textsf{HeteroPCA}$ emerges as a powerful…

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熵正则化最优传输的样本复杂度AI 解读

We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for estimating various quantities of interest, including the entropic regression function, which is a natural analog to the optimal transport map. As an application, we propose a practical model for transfer learning based on entropic optimal transport…

基于 Rademacher 复杂度的差异型近似贝叶斯计算后验集中理论AI 解读

There has been an increasing interest on summary-free solutions for approximate Bayesian computation (abc) that replace distances among summaries with discrepancies between the empirical distributions of the observed data and the synthetic samples generated under the proposed parameter values. The success of these strategies has motivated theoretical studies on the limiting properties of the induced posteriors. However, there is still the lack of a theoretical framework for…

经验部分贝叶斯多重检验与复合卡方决策AI 解读

A common task in high-throughput biology is to screen for associations across thousands of units of interest, for example, genes or proteins. Often, the data for each unit are modeled as Gaussian measurements with unknown mean and variance and are summarized as per-unit sample averages and sample variances. The downstream goal is multiple testing for the means. In this domain, it is routine to “moderate” (i.e., to shrink) the sample variances through parametric empirical…

McKean–Vlasov 模型的贝叶斯非参数推断AI 解读

We consider nonparametric statistical inference on a periodic interaction potential W from noisy discrete space-time measurements of solutions ρ=ρW of the nonlinear McKean–Vlasov equation, describing the probability density of the mean field limit of an interacting particle system. We show how Gaussian process priors assigned to W give rise to posterior mean estimators that exhibit fast convergence rates for the implied estimated densities ρ¯ towards ρW. We further show that…

通过弱条件期望实现随机对象的非线性全局 Fréchet 回归AI 解读

(2019) 691-719) emerges as a special case of our method by choosing a linear kernel. We require that the metric space for the predictor admits a reproducing kernel, while the intrinsic geometry of the metric space for the response is utilized to study the asymptotic properties of the proposed estimates. Numerical studies, including extensive simulations and a real application, are conducted to investigate the finite-sample performance.

检验资产与弱因子AI 解读

ABSTRACT We show that two important issues in empirical asset pricing—the presence of weak factors and the selection of test assets—are deeply connected. Since weak factors are those to which test assets have limited exposure, an appropriate selection of test assets can improve the strength of factors. Building on this insight, we introduce supervised principal component analysis (SPCA), a methodology that iterates supervised selection, principal‐component estimation, and…

场内人工交易重要吗？AI 解读

ABSTRACT Although algorithmic trading now dominates financial markets, some exchanges continue to use human floor traders. On March 23, 2020 the NYSE suspended floor trading because of COVID‐19. Using a difference‐in‐differences analysis around the closure of the floor, we find that floor traders are important contributors to market quality. The suspension of floor trading leads to higher spreads and larger pricing errors for treated stocks relative to control stocks. To…

具有 ARCH 误差的次几何遍历自回归模型AI 解读

In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the Markov chain literature in the 1980s, and it means that the transition probability measures converge to the stationary measure at a rate slower than geometric; this rate is also closely related to the convergence rate of $\beta $ -mixing…

含协变量的秩相似分位数断点回归：识别与推断AI 解读

This study investigates the identification and inference of quantile treatment effects (QTEs) in a fuzzy regression discontinuity (RD) design under rank similarity . Unlike Frandsen et al. (2012, Journal of Econometrics 168, 382–395), who focus on QTEs only for the compliant subpopulation, our approach can identify QTEs and average treatment effect for the whole population at the threshold. We derived a new set of moment restrictions for the RD model by imposing a local rank…

多维聚类依赖下的算法子抽样AI 解读

This paper proposes a novel method of algorithmic subsampling (data sketching) for multiway cluster-dependent data. We establish a new uniform weak law of large numbers and a new central limit theorem for multiway algorithmic subsample means. We show that algorithmic subsampling allows for robustness against potential degeneracy, and even non-Gaussian degeneracy, of the asymptotic distribution under multiway clustering at the cost of efficiency and power loss due to…

时变系数面板模型的设定检验AI 解读

This paper provides nonparametric specification tests for the commonly used homogeneous and stable coefficients structures in panel data models. We first obtain the augmented residuals by estimating the model under the null hypothesis and then run auxiliary time series regressions of augmented residuals on covariates with time-varying coefficients (TVCs) via sieve methods. The test statistic is then constructed by averaging the squared fitted values, which are close to zero…

嵌套模型预测准确性检验的新方法AI 解读

We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to…