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基于 Romano–Wolf 启发式控制错误发现比例的新程序AI 解读

The false discovery proportion (FDP) is a convenient way to account for false positives when a large number $m$ of tests are performed simultaneously. Romano and Wolf [ Ann. Statist. 35 (2007) 1378–1408] have proposed a general principle that builds FDP controlling procedures from $k$-family-wise error rate controlling procedures while incorporating dependencies in an appropriate manner; see Korn et al. [ J. Statist. Plann. Inference 124 (2004) 379–398]; Romano and Wolf…

维度可能增长的多元时间序列协方差估计与线性过程自助法AI 解读

Multivariate time series present many challenges, especially when they are high dimensional. The paper’s focus is twofold. First, we address the subject of consistently estimating the autocovariance sequence; this is a sequence of matrices that we conveniently stack into one huge matrix. We are then able to show consistency of an estimator based on the so-called flat-top tapers; most importantly, the consistency holds true even when the time series dimension is allowed to…

极小极大子矩阵检测的计算障碍AI 解读

This paper studies the minimax detection of a small submatrix of elevated mean in a large matrix contaminated by additive Gaussian noise. To investigate the tradeoff between statistical performance and computational cost from a complexity-theoretic perspective, we consider a sequence of discretized models which are asymptotically equivalent to the Gaussian model. Under the hypothesis that the planted clique detection problem cannot be solved in randomized polynomial time…

大型高斯图模型估计的渐近正态性与最优性AI 解读

The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gaussian graphical model? A novel regression approach is proposed to obtain asymptotically efficient estimation of each entry of a precision matrix under a…

稀疏高斯模型中预测密度的精确极小极大估计AI 解读

We consider estimating the predictive density under Kullback-Leibler loss in an ℓ_{0} sparse Gaussian sequence model. Explicit expressions of the first order minimax risk along with its exact constant, asymptotically least favorable priors and optimal predictive density estimates are derived. Compared to the sparse recovery results involving point estimation of the normal mean, new decision theoretic phenomena are seen. Suboptimal performance of the class of plug-in density…

多元极值中的偏差校正AI 解读

The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is studied in this paper under the multivariate framework. New families of estimators of the stable tail dependence function are obtained. They are asymptotically unbiased versions of the empirical estimator introduced by Huang [Statistics of…

Let $(X_{1},Y_{1}),\ldots,(X_{n},Y_{n})$ be an i.i.d. sample from a bivariate distribution function that lies in the max-domain of attraction of an extreme value distribution. The asymptotic joint distribution of the standardized component-wise maxima $\bigvee_{i=1}^{n}X_{i}$ and $\bigvee_{i=1}^{n}Y_{i}$ is then characterized by the marginal extreme value indices and the tail copula $R$. We propose a procedure for constructing asymptotically distribution-free goodness-of-fit…

高频数据中的纯跳过程检验AI 解读

Pure-jump processes have been increasingly popular in modeling high-frequency financial data, partially due to their versatility and flexibility. In the meantime, several statistical tests have been proposed in the literature to check the validity of using pure-jump models. However, these tests suffer from several drawbacks, such as requiring rather stringent conditions and having slow rates of convergence. In this paper, we propose a different test to check whether the…

稀疏主成分分析的速率最优后验收缩AI 解读

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly orthogonal to the true eigenvector. A sparse structure is then commonly assumed along with a low rank structure. Recently, minimax estimation rates of sparse PCA were established under various interesting settings. On the other side, Bayesian…

论非负无偏估计量AI 解读

We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm yielding almost surely nonnegative unbiased estimators of $f(\lambda)\in\mathbb{R}^{+}$. The study is motivated by pseudo-marginal Monte Carlo algorithms that rely on such nonnegative unbiased estimators. These methods allow “exact…

时变非线性回归模型：非参数估计与模型选择AI 解读

This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this general class of models, an important issue in practice is to address the necessity of modeling the regression function as nonlinear and time-varying. To tackle this, we propose an information criterion and prove its selection consistency…

局部平稳过程中的渐进变化检测AI 解读

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start to change. In many cases, it is of interest to locate the time point where the properties start to vary. In contrast to the analysis of abrupt changes, methods for detecting smooth or gradual change points are less developed and often…

高维非参数回归的极小极大最优估计AI 解读

Minimax $L_{2}$ risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on $d=O(\log n)$ important predictors among a list of $p$ predictors, with $\log p=o(n)$; (2) the true regression surface depends on $O(n)$ predictors but is an additive function where each additive component is sparse but may contain two or more interacting predictors and may have a smoothness…

样本内密度预测的渐近理论AI 解读

This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed. Identification of the density in such regions is guaranteed by structural assumptions on the density that allows exact extrapolation. In this paper, the structural assumption is made that the density is a product of one-dimensional functions. The…

线性时间序列的 Marčenko–Pastur 定律AI 解读

This paper is concerned with extensions of the classical Marčenko–Pastur law to time series. Specifically, $p$-dimensional linear processes are considered which are built from innovation vectors with independent, identically distributed (real- or complex-valued) entries possessing zero mean, unit variance and finite fourth moments. The coefficient matrices of the linear process are assumed to be simultaneously diagonalizable. In this setting, the limiting behavior of the…

高维样本协方差矩阵线性谱统计中心极限定理的替换原理及检验应用AI 解读

Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLTs) for linear spectral statistics of high-dimensional noncentralized sample covariance matrices have received considerable attention in random matrix theory and have been applied to many high-dimensional statistical problems. However, known population mean vectors are assumed for noncentralized sample covariance matrices, some of which even assume Gaussian-like…

不规则间距空间数据的频域经验似然方法AI 解读

This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FDEL) methodology for time series (on a regular grid), the formulation of the spatial FDEL needs special care due to lack of the usual orthogonality properties of the discrete Fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic…

基于正则化典型相关系数的高维独立性检验AI 解读

This paper proposes a new statistic to test independence between two high dimensional random vectors $\mathbf{X}:p_{1}\times1$ and $\mathbf{Y}:p_{2}\times1$. The proposed statistic is based on the sum of regularized sample canonical correlation coefficients of $\mathbf{X}$ and $\mathbf{Y}$. The asymptotic distribution of the statistic under the null hypothesis is established as a corollary of general central limit theorems (CLT) for the linear statistics of classical and…

希尔伯特空间中向量量化的非渐近界AI 解读

Recent results in quantization theory show that the mean-squared expected distortion can reach a rate of convergence of $\mathcal{O}(1/n)$, where $n$ is the sample size [see, e.g., IEEE Trans. Inform. Theory 60 (2014) 7279–7292 or Electron. J. Stat. 7 (2013) 1716–1746]. This rate is attained for the empirical risk minimizer strategy, if the source distribution satisfies some regularity conditions. However, the dependency of the average distortion on other parameters is not…

高维稀疏二元回归的假设检验AI 解读

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate the complexity of the hypothesis testing problem when the design matrix is sparse. We observe a new phenomenon in the behavior of detection boundary which does not occur in the case of Gaussian linear regression. We derive the detection…

利用散射矩分析间歇性过程AI 解读

Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. First- and second-order scattering moments are shown to characterize intermittency and self-similarity properties of multiscale processes. Scattering moments of Poisson processes,…

稀疏主成分分析中的变量选择一致性与无真值假设推断AI 解读

The presence of a sparse “truth” has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the relevant variables be selected consistently if the truth is assumed to be sparse? What can be said about the results of sparse PCA without assuming a sparse and…

This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form $\mathcal{W}_{N}=\Sigma^{1/2}XX^{*}\Sigma^{1/2}$. Here, $X=(x_{ij})_{M,N}$ is an $M\times N$ random matrix with independent entries $x_{ij}$, $1\leq i\leq M$, $1\leq j\leq N$ such that $\mathbb{E}x_{ij}=0$, $\mathbb{E}|x_{ij}|^{2}=1/N$. On dimensionality, we assume that $M=M(N)$ and $N/M\rightarrow d\in(0,\infty)$ as…

极值理论中的分块最大值法：概率加权矩估计AI 解读

In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not been studied thoroughly. The present paper aims at providing conditions under which the BM method can be justified. We also provide a theoretical comparative study of the methods, which is in general consistent with the vast literature on…